. centre de ressources dilemmes et doutes le visage humain de mathématiques Qui sommes-nous Problème de mois activités de promotion babillard
Centrale des maths - centraledesmaths.uregina.ca
Dilemmes & doutes
« D & D »
. .
topic card  



liste de
. .
nouvelle recherche

17 articles trouvés pour ce sujet.
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.
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 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.
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.
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.
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.
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.
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.
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.
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


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

Harley Weston 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.
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.
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.
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 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.
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.




Centrale des maths reçoit une aide financière de l’Université de Regina et de The Pacific Institute for the Mathematical Sciences.



accueil centre de ressources accueil Société mathématique du Canada l'Université de Regina PIMS