Question

Another limit question. Can someone please explain how to do it? I already have the answer.
http://imgur.com/5FO9057

Answer 1

well, since f(x) is composed of 2 different parts, we want to determine what value of a will make the setup not have any jumps or holes in it right?

Answer 2

as the top part goes to +- 1, the value of the top is 2

for what values of a does a^2(-1)^3 = 2
and a^2( 1)^3 = 2

Answer 3

well, its says x=1 so ignore that -1^3 setup :)

Answer 4

might be a little more going on, but thats the basics

Answer 5

the limit from the left is equal to the value of a^2x^3 at x=1
the limit from the right is equal to the value of sqrt(x^2+1) at x=1

if the limits are the same, then it exists.

Answer 6

oh wow i feel like an idiot now lol

Answer 7

thanks for the help :) this site is a life saver.

Answer 8

:) youre welcome