AP Calculus ABhardmcq1 pt

$\lim_{x\to 0}\dfrac{\sqrt{1+x}-\sqrt{1-x}}{x}=$

1

2

\frac{1}{2}

0

Explanation

Core Concept

Rationalize the numerator by multiplying by $\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}$ to get $\frac{(1+x)-(1-x)}{x(\sqrt{1+x}+\sqrt{1-x})}=\frac{2}{\sqrt{1+x}+\sqrt{1-x}}$ . As $x\to 0$ this approaches $\frac{2}{2}=1$ .

Correct Answer

A $1$

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 →

lim⁡x→01+x−1−xx=\lim_{x\to 0}\dfrac{\sqrt{1+x}-\sqrt{1-x}}{x}=limx→0​x1+x​−1−x​​=

Explanation

Core Concept

Correct Answer

More Unit 1: Limits and Continuity practice questions

$\lim_{x\to 0}\dfrac{\sqrt{1+x}-\sqrt{1-x}}{x}=$