







Continuity on a closed interval 
20140921 

Pragya pose la question : The trouble I'm having is as follows :
a continuous function is most of the times defined on a closed interval,
but how is it possible to define it on a closed interval ,because to be continuous at endpoints of the interval the function's
limit must exist at that endpoint,for which it has to be defined in its neighborhood,but we don't know anything about whether the function is always defined in the neighborhood.
Please help... Penny Nom lui répond. 





The continuity of f(x,y)=ln(x^2+y^2) 
20130217 

anu pose la question : the question says we have to find the points in the plane where the function is continuous:
f(x,y)=ln(x^2+y^2) . here we aren't given a particular point (x,y) where we have to check a function's
continuity.
what is to be done if we have to check continuity over the whole domain of the function?
please help . Harley Weston lui répond. 





A limit 
20100927 

norma pose la question : I have a problem like this one but I can get it right. please help me to answer
find the constant a such that the function is continuous on the entire line.
g(x)= {x^2  a^2 / xa if x is not = a
{6 if x = a Penny Nom lui répond. 





Continuity 
20100918 

Carina pose la question : Hi. My name's Carina and I'm currently a sophomore in high school.
I'm having a lot of difficulties in AP Calculus with continuity,
onesided limits, and removable discontinuities. Basically, I have no
idea how to do them or even what they are. I read the lesson but I
still don't get it. Can someone put it in simpler terms so I can
understand how to complete my questions? Thank you! Robert Dawson lui répond. 





A question on continuity 
20070628 

Mac pose la question : f(x) = (1/x) + (1/(2x)) be the function and [0,2] be the interval.
1) It is continuous at the end points ?
2) is f(0) equal to f(2) ? Harley Weston lui répond. 





Continuity of y = x 
20070502 

moulipriya pose la question : Is the curve y =  x  continuous everywhere? Penny Nom lui répond. 





Overlapping circles 
20020529 

Naman pose la question : There are two circles, big circle with radius R and small one with radius r. They intersect and overlap in such a way that the common area formed is 1/2 pi r^{ 2} (half the area of the small circle) If r=1, find the Radius of the big circle (R)? Harley Weston lui répond. 





The average value of a continuous function 
20010508 

Esther pose la question : The average value of a continuous function y = f(x) on the interval [a,b] is given by ________________? Harley Weston lui répond. 





Compounding continuously 
20000321 

Gina pose la question : You deposit $1500 in an account that pays 6.5% annual interest, compounded continuously. Find the balance after 10 years. I'm not sure what to do with the "compounded continuously" part. Penny Nom lui répond. 

