Provide an appropriate response.
-If $x ^ { 3 } \leq f ( x ) \leq x$ for $x$ in $[ - 1,1 ]$, find $\lim _ { x \rightarrow \theta } f ( x )$ if it exists.
A) $- 1$
B) does not exist
C) 0
D) 1

Question

Quizplus · Accepted Answer

Since we have $x^3 \leq f(x) \leq x$ for $x$ in $[-1,1]$, we know that $|f(x)| \leq |x|$ for $x$ in $[-1,1]$. Thus, by the squeeze theorem, we have $$\lim_{x \rightarrow 0} |f(x)| \leq \lim_{x \rightarrow 0} |x| \Rightarrow \lim_{x \rightarrow 0} f(x) = 0.$$ Since $\lim_{x \rightarrow 0} f(x)$ exists and is equal to $0$, we conclude that the answer is (C).

Provide an Appropriate Response x3≤f(x)≤xx ^ { 3 } \leq f ( x ) \leq xx3≤f(x)≤x

Provide an Appropriate Response $x ^ { 3 } \leq f ( x ) \leq x$