016 100 points Consider the function fz z 32 22 Find all t

016 10.0 points Consider the function f(z) = z, ( -3)2, 22 Find all the values of a for which the limit lim () lim f(x) exists, expressing your answer in interval no- tation. 1. (-00,-1)u (-1,2) U (2, 0o) 2. (-00,2) U(2, oo)

Solution

Transition values are x = -1 amd x = 2

Plug in x = -1 into the first two functions :

First :
2 - (-1)
2 + 1
3

Second :
-1

Since they are unequal, the function is DISCONTINUOUS at x = -1

Plug in x = 2 into the second and third functions :

Second :

2

Third :

(2 - 3)^2
(-1)^2
1

So, since they are unequal, the function is DISCONTINUOUS even at x = 2

So, the limit exists everywhere except at -1 and 2

(-infinity , -1) U (-1 , 2) U (2 , infinity)

Option ONE