







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. 





Some continuity questions 
20070628 

From Mac: Can you please help me out to solve this.
problem 1

which of the following statement is true or false ?
a) f(x) = x + [x], x is the member of Z is not continuous at x=0
b) lim x>0+ (f'(x)) = lim x>0 (f'(x))
my doubt here is, what is that [x] in that function ?
problem 2

f(x) = [x] + 1 over positive integer including 0. what is the total number of
point of discontinuities of f(x) ?
Again this [x] confuses me, because if i take [x] this as x, then this function is
continuous. can you please help me out ? Answered by Harley Weston. 





Continuity of y = x 
20070502 

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

