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

AP Calculus ABmediummcq1 pt

$\lim_{x\to 2}\dfrac{x^2-4}{x-2}=$

A.

4

B.

2

C.

0

D.Does not exist

Explanation

Core Concept

Factor the numerator: $\frac{(x-2)(x+2)}{x-2}=x+2$ for $x\ne 2$ . The limit is $2+2=4$ .

Correct Answer

A $4$

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 →