Question

Question on proving continuity

Answer 1

what class is this for?

Answer 2

and what is your understanding of the definition of continuity?

Answer 3

@Peter14, this is from calculus 1. I am quite unsure of the definition, so i came to ask a question regarding about it.

Answer 4

you know about limits already?

Answer 5

for a function to be continuous, \[\lim_{x \rightarrow a+} f(x) = \lim_{x \rightarrow a-} f(x) = \lim_{x \rightarrow a} f(x) = f(a)\]

Answer 6

http://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx is a useful resource

Answer 7

common discontinuities are asymptotes, "holes" in the function with or without accompanying points at a different y-value, and sudden jumps in y-value.

Answer 8

thanks! i'll look at it, what i just dont understand about the question is that, wht is the f(x) function because it wasnt given and how am i suppose to decide if its continuous or not.

Answer 9

the f(x) function is not defined in this case, it is asking about a generalization of all functions for which (f(x))^2 or ^3 are continuous

Answer 10

ah i see, okay i think i kinda get it now. If i make [f(x)]^2=(x)^2. Its not continuous because when u sub x=-1 to f(x)=x <0? but when u sub x=1
\[x \ge0\] so limit is not equal?

Answer 11

you're saying f(x) = x is not a continuous function ?

Answer 12

f(x) = x is a continuous function; so its not a good counter example. pick something else