







Continuity on a closed interval 
20140921 

From Pragya: 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... Answered by Penny Nom. 





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

From anu: 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 . Answered by Harley Weston. 





A limit 
20100927 

From norma: 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 Answered by Penny Nom. 





Continuity 
20100918 

From Carina: 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! Answered by Robert Dawson. 





A question on continuity 
20070628 

From Mac: 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) ? Answered by Harley Weston. 





Continuity of y = x 
20070502 

From moulipriya: Is the curve y =  x  continuous everywhere? Answered by Penny Nom. 





Overlapping circles 
20020529 

From Naman: 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)? Answered by Harley Weston. 





The average value of a continuous function 
20010508 

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





Compounding continuously 
20000321 

From Gina: 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. Answered by Penny Nom. 

