Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question

AP Calculus ABhardmcq1 pt

Suppose $x^3\le f(x)\le x$ for all $x$ in $(0,1)$ . What is $\lim_{x\to 0^+} f(x)$ ?

A.

1

B.

\frac{1}{2}

C.Cannot be determined from the information given

D.

0

Explanation

Core Concept

Both $x^3$ and $x$ approach $0$ as $x\to 0^+$ . Since $f$ is trapped between them, the Squeeze Theorem gives $\lim_{x\to 0^+} f(x)=0$ .

Correct Answer

D $0$

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