Question

I have an ACT practice guide problem that I need answered and explainedIt has a list of answers to choose from I will list that belowA. 1B. -2C. 4D. The limit does not exist.

Answer 1

SOLUTION

The limit of a function at a point aa in its domain (if it exists) is the value that the function approaches as its argument approaches a.

The limit of a function F exist if and only if

$\begin{gathered} \lim _{x\rightarrow x^+}f(x)=\lim _{x\rightarrow x^-}f(x) \\ \\ \text{The left-hand limit =The Right-hand Limit} \end{gathered}$

Considering the image given, the limit of the function from the left is from the first graph

$\lim _{x\rightarrow1^-}f(x)=4\Rightarrow\text{ The left hand limit}$

Similarly, the limit of f(x) from the right-hand side is on the second graph

$\lim _{x\rightarrow1^+}f(x)=-2\Rightarrow The\text{ Right -hand limit}$

Since

$\begin{gathered} \text{Left-hand limit}\ne Right\text{ hand imit} \\ 4\ne-2 \end{gathered}$

Therefore

The Limit does not exist (D)