AP Calculus ABhardmcq1 pt

$\lim_{x\to\infty}\left(\sqrt{x^2+2x}-x\right)=$

0

1

2

\infty

Explanation

Core Concept

Rationalize: $\sqrt{x^2+2x}-x=\frac{(x^2+2x)-x^2}{\sqrt{x^2+2x}+x}=\frac{2x}{\sqrt{x^2+2x}+x}$ . Dividing numerator and denominator by $x$ gives $\frac{2}{\sqrt{1+2/x}+1}\to\frac{2}{2}=1$ .

Correct Answer

B $1$

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lim⁡x→∞(x2+2x−x)=\lim_{x\to\infty}\left(\sqrt{x^2+2x}-x\right)=limx→∞​(x2+2x​−x)=

Explanation

Core Concept

Correct Answer

More Unit 1: Limits and Continuity practice questions

$\lim_{x\to\infty}\left(\sqrt{x^2+2x}-x\right)=$