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Une autre bille de rayon différent 2002-02-27
Sarah pose la question :
une bille de 6 cm repose au fond d'1 cylindre droit dont la base est un disque de rayon 10 cm. On verse de l'eau dans le cylindre de façon à recouvrir exactement la bille. Démontrez que l'on peut remplacer la bille par une autre bille de rayon différent (mais supérieur) de sorte que l'eau initialement versée recouvre exactement cette nouvelle bille
Claude Tardif lui répond.
Average price 2017-09-15
Annette pose la question :
If I sold a widget at $15.50 17.5% of the time and $16.50 88.5% of the time what is the algebraic expression for that. How do I arrive at an average price
Penny Nom lui répond.
Differentiate y = x^x^x 2017-03-19
Nafis pose la question :
differentiate y = x^x^x
Penny Nom lui répond.
The derivative of the inverse of a function 2016-10-28
Kate pose la question :
Hi, I'm in a College level Calculus course and I can't seem to figure out the answer to this question.
Find the derivative of f^-1(4) if f(3)=4 and f'(3)=1/7

Penny Nom lui répond.
Subtraction of two numbers in different bases 2016-10-07
Wica pose la question :
Hello,

So happy I found this site. I am having problems with bases. My question is :
Please perform the subtraction between two number over different bases :
A. (5874)base 12 - (216)base 9
B. (216)base 9 - (5874)base 12

Penny Nom lui répond.
Implicit differentiation 2016-06-06
Pranay pose la question :
Is a circle x^2+y^2=2 a function? If it is not a function, why is it possible to do implicit differentiation on it?
Thanks.

Penny Nom lui répond.
A tangent line to a parabola 2015-12-02
pei pose la question :
Given that the line y=mx-5 is a tangent to the curve y=2x^2+3 find the positive value of M.
Penny Nom lui répond.
The derivative of x^1/3 2015-11-08
omar pose la question :
hi can help me
am teacher ask me about x^1/3 Derivation definition .

Penny Nom lui répond.
Two cars approaching an intersection 2015-04-16
Engabu pose la question :
Car A is traveling west at 50km/h & car B is traveling north at 60km/h. both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 3km & car B is 4km from the intersection?
Penny Nom lui répond.
Integers in different bases 2015-03-05
Michael pose la question :
Let k be a positive integer so that 28 (subscript)k = 132 (subscript)5
Penny Nom lui répond.
f(x)=(x^2-1)/(x-1) 2015-02-21
Ahmed pose la question :
Is f(x)=[(x^2-1)/(x-1) and x=2 at x=1] differentiable at x=1 ? Why ?
Penny Nom lui répond.
Differentiate ln[x(2x-4)^1/2] 2014-06-28
Igwe pose la question :
If y=In[x(2x-4)^1/2],find dy/dx at x=3
Penny Nom lui répond.
A tangent of the curve (x/a)^n+(y/b)^n =2 2014-04-15
sudhir pose la question :
the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is
Penny Nom lui répond.
A number with all the digits different 2014-02-07
Jon pose la question :
I'm not a mathematician but just curious. Is there a name for a number of up to ten digits where each digit is different, i.e the equivalent of an isogram in linguistics? My online banking gives me a random 8-digit number each time I log on and it is rare to get one of the type I refer to. There must be calculable odds, but I'm only allowed one question!
Thanks in advance
Jon

Harley Weston lui répond.
Differentiate x^x - 2^sinx 2013-08-09
tarun pose la question :
derivative of x^x - 2^sinx
Penny Nom lui répond.
f(x) + f ''''(x)=0 2013-03-05
Andreea pose la question :
Hei. I don’t speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something.
Brennan Yaremko lui répond.
The multiplication table for the different bases 2013-02-01
sylvia pose la question :
I am having a difficult time trying to figure out how to fill in the multiplication table for the different bases. i don't know how to get the numbers.
Penny Nom lui répond.
The derivative of y = sin (30º + x) 2012-11-07
Saskia pose la question :
derivative of y = sin (30º + x)
Harley Weston lui répond.
An implicit differentiation problem 2012-10-26
Katie pose la question :
find y' of x^2y-2y^3=3x+2y
Harley Weston lui répond.
Differentiation rules 2012-10-23
Morgan pose la question :
Use the derivative rules to differentiate each of the following:
1. f(x)=1/x-1
2. f(x)= sqrt(x)

Penny Nom lui répond.
The derivative of 2sin cubed x - 3 sin x 2012-03-25
holly pose la question :
suppose f(x) = 2sin cubed x - 3 sin x

show that f 1(x) = -3 cos x cos 2x

Harley Weston lui répond.
Integral 1/(25-x^2)^3/2 2012-02-22
John pose la question :
Integral 1/(25-x^2)^3/2
Harley Weston lui répond.
Dt[sin t tan (t^2+1)] 2012-02-21
Ayu pose la question :
Ayu
Dt[sin t tan (t^2+1)]
derivatives

Harley Weston lui répond.
Notation for the second derivative 2012-02-06
Shafira pose la question :
In all math textbooks, it is written that d/dx ( d/dx) (y)= d2y/dx2. Why do they write it as d2y/dx2, not as d2y/d2x2?
Robert Dawson lui répond.
The derivative of x^-(1/2) 2012-01-14
Eric pose la question :
I have an problem figuring out the derivative of the negative square root of x i.e. x^-(1/2) using the first principle.
Could someone please show me?
Thanks in advance!

Harley Weston lui répond.
The number of digits in a number base m 2011-12-22
Jash pose la question :
Assume there is a number system of base m.

The one property of this system is: If 2 numbers written in this system, which have 'a' and 'b' as the number of digits are multiplied, then the product of the 2 numbers will have a number of digits which is a function f(a,b).

In other words, as long as the number of digits of the 2 numbers are constant, the number of digits of their product is a constant.

Find m.

Robert Dawson lui répond.
Implicit differentiation 2011-10-20
Monica pose la question :
Find dy/dx in terms of x and y, if sin(xy)=(x^2)-y.
Penny Nom lui répond.
The derivative of f(x) = (x+1)^1/2 2011-09-05
Carla pose la question :
Find the derivative using the limit process of
f(x) = (x+1)^1/2

Harley Weston lui répond.
Differentiable on an interval 2010-08-12
Dave pose la question :
Hi I was wondering if a function can be differentiable at its endpoint. For example if I have Y = X^2 and it is bounded on closed interval [1,4], then is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4). They always say in many theorems that function is continuous on closed interval [a,b] and differentiable on open interval (a,b) and an example of this is Rolle's theorem. Thank you for your help.
Robert Dawson lui répond.
The rate of change of y with respect to x 2010-04-29
Tom pose la question :
I just had a quick calc question about wording that wasn't ever addressed in class. When the book says "the rate of change of y with respect to x", should it be considered how fast y is changing in comparison to x?

I ask because the textbook says that "y is changing 3 times faster than x, so the rate of change of y with respect to x is 3." I'm use to rate being like velocity, as in units of distance per units of time. All we're told in class is that it's the slope of the tangent line, I was hoping you could clarify for me what exactly is meant by the wording of a "rate of change of something with respect to something else". More specifically, what "rate" and "with respect to" mean within this context?

Thanks for your time

Harley Weston lui répond.
The derivative of cos^3x 2010-04-06
Erson pose la question :
Find y' of the given function: y = cos^3x.
Harley Weston lui répond.
The nth derivative of x^(n-1) log x 2010-03-10
shambodeb pose la question :
This is a successive differentiation problem by Leibnitz theorem

If y = xn-1 log x ; Proof nth derivative y(n) = (n-1)!/x

Harley Weston lui répond.
Painting a dome 2009-10-30
Jessica pose la question :
A hemispherical dome with a radius of 50 ft will be given a coat of paint .01 inch thick. The Contractor for the job wants to estimate the number of gallons of paint needed. Use a differential to obtain an estimate (231 cubic inches/gallon) HINT: Approximate the change in volume of hemisphere corresponding to increase of .01 inch in the radius.
Robert Dawson lui répond.
Differentiating y= square root(x-1) 2009-09-29
edith pose la question :
describe the x-values at which f is differentiable.
y= square root(x-1)

Penny Nom lui répond.
Maximum Volume of a Cylinder Inscribed in a Sphere 2009-06-18
Jim pose la question :
Hello I have a hard time finishing this question: A right circular cylinder has to be designed to sit inside a sphere of radius 6 meters so that each top and bottom of the cylinder touches the sphere along its complete circular edge. What are the dimensions of the cylinder of max volume and what is the volume?
Janice Cotcher lui répond.
differentiate y sin[x^2]=x sin[y^2] 2009-05-11
mamiriri pose la question :
derivate y sin[x^2]=x sin[y^2]
Harley Weston lui répond.
Implicit differentiation 2009-03-01
Emily pose la question :
determine the derivative y' at the point (1,0)
y= ln(x^2+y^2)

y'(1)= ??

Stephen La Rocque lui répond.
Multiplying in different bases 2009-02-25
Susan pose la question :
11 base 2 X 22 base 3 + 33 base 4 = _________ base 5
Robert Dawson lui répond.
Implicit differentiation 2009-02-18
Sunny pose la question :
Find slope of the tangent line to the curve 2(x^2+y^2)2=25(x^2–y^2) at (3,-1)
Robert Dawson and Harley Weston lui répond.
In what base is 3x3= 10? 2009-02-14
David pose la question :
In what base is 3x3= 10, 3x3=11, 3x3 = 12? is there a fast way to see this or do I have to create multiplication tables until I find the right one?
Penny Nom lui répond.
What's the derivative of y = e^2x-e^-2x / e^2x+e^-2x? 2009-02-02
Heather pose la question :
What's the derivative of y = e^2x-e^-2x / e^2x+e^-2x ?
Harley Weston lui répond.
Determine y'' by implicitly differentiating twice 2009-01-04
Walter pose la question :
Given x^3 - 3xy + y^3 = 1 , determine y'' by implicitly differentiating twice. I cannot solve this. Would you be kind enough to perform the mathematics and show the steps involved in obtaining the solution?
Harley Weston lui répond.
Division in different bases 2008-12-02
MICHELLE pose la question :
DIVIDE 538 BY 14 IN BASE 2, 3, 4 & 5
Penny lui répond.
Separating variables 2008-11-04
Terry pose la question :
by separating variables solve the initial value problem

(x+1)y' + y = 0 y(0) = 1

Harley Weston lui répond.
Antiderivative of 1/(x(1 - x)) 2008-10-22
Matt pose la question :
derivative of dx/(x(1-x))

From what I've seen I should break apart the equation as such derivative of dx/x - dx/(1-x) and then get the 2 corresponding log functions.

If that is correct why does this factoring work, if that is incorrect what is the proper way to find the derivative.

Harley Weston lui répond.
Concavity and the second derivative 2008-10-15
Christina pose la question :
I'm having trouble solving for a second derivative for the following graphing question.

f(x) = (X^2+2x+4)/2x

using the quotient rule, I found:
f'(x) = (x^2-4)/(2x^2)

however, using the quotient rule again I can't seem to solve it (concavity):
f'''(x)=[(2x)(2x^2)-(x^2-4)(4x)]/[(2x^2)^2]
f''(x)=[(4x^3-(4x^3 -16x)]/4x^4
f''(x)=16x/4x^4
f''(x)=4/x^3

and making the equation equal to zero result in 0=4 which doesn't seem to make sense...

Penny Nom lui répond.
A different approach to a word problem 2008-10-03
Kenneth pose la question :
Sarah's age is 2/3 of Mary's age and 3/4 of Ruth's age. The sum of their ages is 46 years. How old is each?
Penny Nom lui répond.
What is the derivative of (2^sinx)/(logbase4(2x+1))? 2008-09-16
Jesse pose la question :
What is the derivative of (2^sinx)/(logbase4(2x+1))
Harley Weston lui répond.
Trough Filling with Water 2008-08-21
lanny pose la question :
a triangular trough is 10 feet long, 6 feet across the top, and 3 feet deep. if water flows at the rate of 12 cubic inches per minute, find how fast the surface is rising when the water is 6 inches deep.
Janice Cotcher lui répond.
A series solution of y' = xy 2008-07-03
sasha pose la question :
I've to find the power series solution of the differential equation: y' = xy.
I don't know how to find the recursive equation. Can you please help me. Thanks

Harley Weston lui répond.
Differentiate y= (x^x^x)^x 2008-06-27
emril pose la question :
Differentiate y= (x^x^x)^x
Harley Weston lui répond.
f(x)=sin^3(3x^2) find f ' (x) 2008-04-21
Michael pose la question :
f(x)=sin^3(3x^2) find f ' (x)
Harley Weston lui répond.
The chain rule 2008-04-10
joey pose la question :
pls help me to Differentiate
y=(3x^2-4x)^8

Harley Weston lui répond.
Differentiate 2007-12-28
taiwo pose la question :
i am finding it difficult to use first principle to differentiate this question: y=xcos2x. can u help me.
Penny Nom lui répond.
The tangent to a curve 2007-12-10
Christy pose la question :
I know this question is simple but I can't figure out what I'm doing wrong.
Find the equation of the tangent line to the curve 2x^2 - y^4= 1 at the point (1,1).

Penny Nom lui répond.
The derivative 2007-11-19
ralf pose la question :
Find the derivative of the function
1-. y=1+2x8
2-. y=(1+2x )8

Harley Weston lui répond.
f(x+y) = f(x) + f(y) + 2xy 2007-11-01
Marcia pose la question :
For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as h -> 0 of f(h) / h = 7, find: f(0), use the definition of the derivative to find f'(x), and find f(x).
Penny Nom lui répond.
The rate of change of the concentration of a solution 2007-10-30
Nicholas pose la question :
A barrel initially has two kg of salt dissolved in twenty liters of water. If water flows in the rate of 0.4 liters per minute and the well-mixed salt water solution flow out at the same rate, how much salt is present after 8 minutes? I tried working backwards given the answer but I can't seen to get their answer of ~1.7kg. Any help would be great! Thanks
Harley Weston lui répond.
The derivative of f(x)=1/(x-1) 2007-09-21
Michelle pose la question :
im having trouble finding the derivative of f(x)=1/(x-1) using the f(x+h)-f(x)/h method.
Stephen La Rocque lui répond.
Differentiate x^(1/3) using first principles 2007-09-14
Sheila pose la question :
our teacher gave us this question as a challenge and even he couldnt figure it out: Differentiate x^(1/3) [aka the cube root of x] using first principles. i know the answer is 1/(3.x^2/3), but how is it possible using first principles?
Harley Weston lui répond.
Solve y'' + y = 0 2007-07-28
Shih-ya pose la question :
How do you solve y’’ + y = 0
Stephen La Rocque and Harley Weston lui répond.
Implicit Derivatives 2007-07-13
Charles pose la question :
I need help computing y' by implicit differentiation the question is: y^2 + x/y + 4x^2 - 3
Stephen La Rocque lui répond.
sin|x| and cos|x| 2007-06-25
Mac pose la question :
Can anyone tell me whether sin|x| and cos|x| is differentiable at x=0 ? As far as i know, cos(x) and sin(x) is differentiable at all x.
Penny Nom and Stephen La Rocque lui répond.
The second derivative 2007-04-14
Gerry pose la question :
In mathematical context,what do you understand by the term "Second Derivative"
Penny Nom lui répond.
What is the intensity 5m below the surface? 2007-03-31
david pose la question :
I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help.
Penny Nom lui répond.
The period of a simple pendulum 2007-03-10
Melissa pose la question :
The period of a simple pendulum of length L feet is given by: T=2pi(sqrt(L/g))seconds. It is assumed that g, the acceleration due to gravity on the surface of the earth, is 32 feet per second per second. If the pendulum is a clock that keeps good time when L=4 feet, how much time will the clock gain in 24 hours if the length of the pendulum is decreased to 3.97 feet? (Use differentials and evaluate the necessary derivative at L=4 feet.) Answer is in seconds. Melissa
Penny Nom lui répond.
Derivatives 2007-02-01
Jacob pose la question :
Find the derivative of: y= pi^2+x^2+3xy+sin(y^2)
Penny Nom lui répond.
Water is being pumped into the pool 2006-10-24
Jon pose la question :
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deeps at the deep end. Water is being pumped into the pool at 1/4 cubic meters per minute, an there is 1 meter of water at the deep end.

a) what percent of the pool is filled?

b) at what rate is the water level rising?

Stephen La Rocque lui répond.
Differentiate Y= sin3x + cos7x 2006-08-22
james pose la question :
Differentiate the function of x using the basic rules.

Y= sin3x + cos7x

Stephen La Rocque lui répond.
differentiate the volume of a cylinder with V respect to h 2006-05-24
A student pose la question :
differentiate the volume of a cylinder with V respect to h
Stephen La Rocque lui répond.
Rate of ladder falling 2006-04-30
Harsh pose la question :
A ladder 4 m long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 30 cm/s, how quickly is the top of the ladder sliding down the wall when the bottom of the ladder is 2 m from the wall?
Stephen La Rocque lui répond.
Differentiation, powers and logs 2006-01-06
Claudia pose la question :

Question: how do I find the derivative of

x* ln(x+(e^2))^2

x^lnx

x^(e^(-x^2))


Penny Nom lui répond.
Notation for the second derivative 2005-11-08
Mussawar pose la question :
my question is d/dx( dy/dx) = d2y/dx2. why it is not equal to d2y/d2x.
Penny Nom lui répond.
Velocity and acceleration 2005-10-27
Candace pose la question :
When taking the integral of the position function, you get the velocity function, and the same for velocity to acceleration. So when you do each of these, you get a function. But when you integrate on a graph, you get an area under a curve. The area is un units squared- where do the units go when you make it an equation? How can a function be an area?
Harley Weston lui répond.
Can we take the derivative of independent variable 2005-10-18
Mussawar pose la question :
why we take derivative of dependent variable with respect to independent variable .can we take the derivative of independent with respect to dependent.if not why.
Walter Whiteley lui répond.
U'(X) - U(X) = 0; U(0) = 2 2005-09-23
David pose la question :
Out of interest could you please answer the following questions?

U'(X) - U(X) = 0; U(0) = 2

and

U''(X) - U'(X) = 0; U'(0) = U(0) = 2


Harley Weston lui répond.
How do you differentiate y=(x)^(x^x)? 2005-09-14
Calebius pose la question :
How do you differentiate y=(x)(xx)?
Penny Nom lui répond.
Logarithmic differentiation 2005-05-23
Richard pose la question :
I need to convince myself that I understand the process of differentiating y=xx.
The specific question is that if I have to take the logarithm of both sides of the equation how can differentiate the following?
y= {(x+2)(x+2)}/{(x+1)(x+1)} - {(x+1)(x+1)}/(xx),
I have an idea that the differential of this fairly complex function is itself ... am I right or wrong.

Penny Nom lui répond.
Differentiating F(x,y) = 0 2005-01-23
Jacob pose la question :
In calculus, we often mention to the students that if F(x,y) = 0, then we can differentiate both sides and still get an equality. The problem is that we can't perform the same operation on F(x) = 0, say x = 0, otherwise 1 = 0, which is absurd. What is the reason?
Walyer Whileley and Harley Weston lui répond.
ln(x)/x 2004-12-11
Tina pose la question :
What is the derivative of (ln x)/x? The double derivative?
Penny Nom lui répond.
An ODE 2004-11-10
David pose la question :
I have a question that i really cant do, it is as follows:

The ODE dy/dx + 0.5y = 0.5e^(-1.5x) ; y(5) = 2

Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6

Harley Weston lui répond.
Implicit differentiation 2004-10-24
Emily pose la question :
If x^3+3xy+2y^3=17, then in terms of x and y, dy/dx =
Penny Nom lui répond.
differentiate Y=X^X^X 2004-09-13
Kunle pose la question :
differentiate Y=X^X^X
Penny Nom lui répond.
The integrating factor method 2004-08-05
A student pose la question :
Whilst using the integrating factor method, I am required to integrate a function multipled by another function.

say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.

Integral f(t)*g(t) dt or Integral exp(kt)*g(t) dt

What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k? More specifically, the problem and my attempted answer is in PDF format:

In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function.

Harley Weston lui répond.
Differentiation 2004-08-04
A parent pose la question :
I am a parent trying to understand higher level of maths and would be very grateful if you could help with differentiating the following functions, identifying general rules of calculus:

a) f(x)=e^2^xIn(cos(8x))

b) f(x)=secx/SQRTx^4+1

Penny Nom lui répond.
Some calculus problems 2004-04-01
Weisu pose la question :

I have questions about three word problems and one
regular problem, all dealing with derivatives.

  1. Find all points on xy=exy where the tangent line
    is horizontal.
  2. The width x of a rectangle is decreasing at 3 cm/s,
    and its length y is increasing at 5 cm/s. At what rate
    is its area A changing when x=10 and y=15?
  3. A car and a truck leave the same intersection, the
    truck heading north at 60 mph and the car heading west
    at 55 mph. At what rate is the distance between the
    car and the truck changing when the car and the truck
    are 30 miles and 40 miles from the intersection,
    respectively?
  4. The production P of a company satisfies the
    equation P=x2 + 0.1xy + y2, where x and y are
    the inputs. At a certain period x=10 units and y=8
    units. Estimate the change in y that should be made to
    set up a decrease of 0.5 in the input x so that the
    production remains the same.

If you could just give me some hints on these
questions, I'd really appreciate it. Thanks!


Penny Nom lui répond.
A derivative 2004-03-31
A student pose la question :
What is the nth derivative of f(x) =(2x)/(1-(x2))?
Harley Weston lui répond.
A partial derivative 2004-03-19
Penny Nom pose la question :
Is it possible to differentiate the following equation, if so could you please explain.

S=SQRT(T-(5/X^2))

I would like the derivative of S with respect to X.

Harley Weston lui répond.
The derivative of x to the x 2004-02-14
Cher pose la question :
what about the derivative of x to the power x?
Penny Nom lui répond.
The slope of a tangent 2003-10-01
A student pose la question :

find the slope of the tangent to each curve at the given point

f(x)=square root 16-x, where y=5


Penny Nom lui répond.
Differentiating inverses 2002-11-20
Amy pose la question :
f(x)= x3+x+1, a=1 find g'(a) (g = f -1). I am having trouble finding g(a).
Penny Nom lui répond.
Undetermined coefficients 2001-11-22
Hoda pose la question :
The equation is:

y" - 2y' + y = t et + 4

We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Atet+Bet+C, but all I get is C=4 and I tried (At2+Bt+C)et+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions?


Harley Weston lui répond.
A tangent line 2001-11-21
A student pose la question :
write an equation of the line tangent to the graph of

ey + ln(xy) = 1 + e at (e,1)

Harley Weston lui répond.
4 sinx cosy = 1 2001-10-10
A student pose la question :
How would i differentiate the following example in terms of t (x and y are functions of t)

4 sinx cosy = 1


Claude Tardif lui répond.
(x^2-5x-6)/(x-6) 2001-10-02
Bill pose la question :
given f(x) = (x2-5x-6)/(x-6) find f'(6).
Harley Weston lui répond.
National consumption function 2001-05-09
Brian pose la question :
If consumption is $11 billion when disposable income is 0 and the marginal propensity to consume is dC/dy = 1/(2y+4)1/2+0.3(in billions of dollars), find the national consumption function.
Harley Weston lui répond.
Differentiation 2001-04-17
Esther pose la question :
Could you please tell me what the first derivative is of the following:

y = 2/(2x+e2x)

Is it (1+xe2x)/(2x+e2x)2 or perhaps -4(1+e2x)/(2x+e2x)2 ? I am a little confused between the two!


Harley Weston lui répond.
Airflow in windpipes 2001-03-25
Ena pose la question :
The volume of air flowing in windpipes is given by V=kpR4, where k is a constant, p is the pressure difference at each end, R is the radius. The radius will decrease with increased pressure, according to the formula: Ro - R = cp, where Ro is the windpipe radius when p=0 & c is a positive constant. R is restricted such that:
0 < 0.5*Ro < R < Ro,
find the factor by which the radius of the windpipe contracts to give maximum flow?

Harley Weston lui répond.
A jogger 2001-03-12
Bill pose la question :
At time t=0 a jogger is running at a velocity of 300 meters per minute. The jogger is slowing down with a negative acceleration that is directly propotional to time t. This brings the jogger to a stop in 10 minutes.

a) write an expression for the velocity of the jogger at time t.

b) what is the total distance traveled by the jogger in that 10-minute interval.


Harley Weston lui répond.
The domain of the derivative 2001-02-22
Wayne pose la question :
I know that the domain of f'(x) is a subset of the domain of f(x). Is it necessarily true that the subset will have at most one less element than the domain of the original function?
Harley Wesston lui répond.
Differentiation of y = x n 2001-02-17
Jashan pose la question :
i am studying differentation at the moment i have drawn some graphs such as y=x 2. i have found the formula for the gradient of this curve, this being 2x obtained by using differentation, but i need to know the general case for the formula where y=xn in order for me to understand this topic more throughly, i would also like to know how u derived this general formula
Harley Weston lui répond.
Find an exprression for f(x) 2001-02-07
A 12th grade AP Calc student pose la question :
Let f be the function defined for all x > -5 and having the following properties. Find an expression for f(x).

i) f ''(x) = 1/ (x+5)1/3 for all x in the domain of f

ii) the line tangent to the graph of f at (4,2) has an angle of inclination of 45 degress.


Harley Weston lui répond.
How do you integrate secant(theta)? 2000-12-22
Robert Williamson pose la question :
How do you integrate secant(theta)?

I know the answer is ln [sec(theta) + tan(theta)] but how do you get there?


Claude tardif lui répond.
Derivatives, there must be an easier way 2000-09-06
Brad Goorman pose la question :
The direction read: Take the derivative of each expression.

y = {1+[x+(x2 +x3)4]5}6


Harley Weston lui répond.
A derivative problem 2000-06-04
Jeff Ellis pose la question :
If F(x)=(4+x)(3+2x2)2(2+3x3)3, find F'(0)
Harley Weston lui répond.
Thearcius Functionius 2000-05-03
Kevin Palmer pose la question :
With the Olympics fast approaching the networks are focusing in ona new and exciting runner from Greece. Thearcius Functionius has astounded the world with his speed. He has already established new world records in the 100 meter dash and looks to improve on those times at the 2000 Summer Olympics.

Thearcius Functionius stands a full 2 meters tall and the networks plan on placing a camera on the ground at some location after the finish line(in his lane) to film the history making run. The camera is set to film him from his knees(0.5 meters up from the ground) to 0.5 meters above his head at the instant he finishes the race. This is a total distance of two meters(the distance shown by the camera's lens).
Harley Weston lui répond.

An indefinite integral 2000-05-03
Bonnie Null pose la question :
I am to find the indefinite integral of: (ex - e-x)2 dx
Claude Tardif lui répond.
y = x^x^x^x... 2000-04-05
Michael Hackman pose la question :
Find the derivative of: y = x^x^x^x... on to infinity.
Claude Tardif lui répond.
A mixture problem 2000-03-06
Rebecca Edwards pose la question :
A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t.
Harley Weston lui répond.
A calculus problem 1999-12-08
JT Wilkins pose la question :
These are the questions:

  1. Show that there exists a unique function that meets the following requirements:

    a) f is differentiable everywhere
    b) f(0)= f'(0)= 0
    c) f(x+y)= f(x)+ f(y), for all real values of x,y

  2. Consider the function F: R-->R (All Reals)

    F(x) = 0, for x irrational & 1/q, x=p/q gcd(p,q)=1 q > 0

    a)determine the values x where f is continuous, respectively discontinuous.
    b)determine the values x when f is differentiable and for each of these values compute f'(x).


Penny Nom lui répond.
The chain rule 1999-12-03
Jennifer Stanley pose la question :
This problem is making me dizzy. I would greatly appreciate a little help!

Express the derivative dy/dx in terms of x.

y=u^2(u-u^4)^3 and u=1/x^2
Harley Weston lui répond.

Two calculus problems 1999-12-01
O'Sullivan pose la question :
Question #1 Assume that a snowball melts so that its volume decreases at a rate proportional to its surface area. If it takes three hours for the snowball to decrease to half its original volume, how much longer will it take for the snowball to melt completely? It's under the chain rule section of differentiation if that any help.

I've set up a ratio and tried to find the constant but am stuck.

Question #2 The figure shows a lamp located three units to the right of the y-axis and a shadow created by the elliptical region x^2 + 4y^2 < or= 5. If the point (-5,0) is on the edge of the shadow, how far above the x axis is the lamp located?

The picture shows an x and y axis with only the points -5 and 3 written on the x axis. the lamp is on the upper right quadrant shining down diagonally to the left. There's an ellipse around the origin creating the shadow. It's formula is given as x^2 + 4y^2=5.


Harley Weston lui répond.
Two derivatives 1999-11-16
Gina Renicker pose la question :
The derivative of:

y=e(xlnx) and y=x2arctan(x1/2)
Harley Weston lui répond.

Clockwise or Counterclockwise? 1999-10-27
Tim pose la question :
A particle moves around the circle x2 + y2 = 1 with an x-velocity component dx/dt = y
  1. Find dy/dt

  2. Does the particle travel clockwise or counterclockwise around the circle? Why?

Harley Weston lui répond.
Derivatives with logs 1999-10-26
Kate pose la question :
What is the derivative of 5 to the 5x-2 at x equals 0.8?
Harley Weston lui répond.
Parametric Equations 1999-08-06
Nicholas Lawton pose la question :
Show that an equation of the normal to the curve with parametric equations x=ct y=c/t t not equal to 0, at the point (cp, c/p) is :

y-c/p=xp^2-cp^3
Harley Weston lui répond.

A calculus problem 1999-07-22
Nicholas Lawton pose la question :
The curve y= e^x(px^2+qx+r) is such that the tangents at x=1 and x=3 are parallel to the x-axis. the point (0,9) is on the curve. Find the values of p,q and r.
Harley Weston lui répond.
Related rates 1999-05-13
Tammy pose la question :
The sides of a rectangle increase in such a way that dz/dt=1 and dx/dt=3*dy/dt. At the instant when x=4 and y=3, what is the value of dx/dt? (there is a picture of a rectangle with sides x and y, and they are connected by z, which cuts the rectangle in half)
Harley Weston lui répond.
Graphing the Derivative 1999-01-18
Milena Ghebre pose la question :
This question has been nagging me for sometime now.

Is there a way of finding out the derivative of a function, just by looking at the graph of it?
Walter Whiteley lui répond.

Calculus 1999-01-16
Kaylea Rankin pose la question :
Differentiate the following.

y = 1 /(2+3/x)
Jack LeSage and Penny Nom lui répond.

The area and the circumference of a circle. 1998-08-27
Jason Wright pose la question :
I was looking at the relationship of the area of a circle and the circumference when I realized that 2*pi*r is the derivative of pi*r^2. I was wondering if there is any connective deep dark meaning as to why this appears to be related. Thanks for any help you can give me!
Walter Whiteley lui répond.
A Tightrope Walker. 1998-02-19
Amy Zitron pose la question :
A tightrope is stretched 30 feet above the ground between the Jay and the Tee buildings, which are 50 feet apart. A tightrope walker, walking at a constant rate of 2 feet per second from point A to point B, is illuminated by a spotlight 70 feet above point A....
Harley Weston lui répond.
Mathematical Induction and the Derivative 1997-03-18
Shuling Chong pose la question :
"Obtain a formula for the nth derivative of the product of two functions, and prove the formula by induction on n."

Any educated tries are appreciated.
Penny Nom lui répond.

 
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