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

AP Calculus ABeasymcq1 pt

If $f$ is continuous at $x=2$ and $f(2)=8$ , then $\lim_{x\to 2} f(x)=$

A.

0

B.

8

C.

16

D.Does not exist

Explanation

Core Concept

Continuity at $x=2$ means $\lim_{x\to 2} f(x)=f(2)$ . Since $f(2)=8$ , the limit equals $8$ .

Correct Answer

B $8$

More Unit 1: Limits and Continuity practice questions

hardLet $f(x)=\begin{cases} x^2+ax, & x<1 \\ bx+3, & x>1 \end{cases}$. If $f(1)=2$ and $f$ is continuous at $x=1$, what is $a+b$?
hardSuppose $x^3\le f(x)\le x$ for all $x$ in $(0,1)$. What is $\lim_{x\to 0^+} f(x)$?
hard$\lim_{x\to 0} x^2\sin\left(\frac{1}{x}\right)=$
hardSuppose $f$ is continuous on $[0,3]$ with $f(0)=-4$ and $f(3)=1$. Which statement is guaranteed by the Intermediate Value Theorem?
hardLet $f(x)=x^3-x-1$. Given that $f(1)=-1$ and $f(2)=5$, which interval is guaranteed to contain a zero of $f$ by the Intermediate Value Theor…

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 1: Limits and Continuity Questions →