Evaluate the limit. $\lim _{x \rightarrow \infty}\left(x-\sqrt{x^{2}+2}\right)$
A) -2
B) 1
C) 0
D) 2

Question

Quizplus · Accepted Answer

We can simplify the expression inside the limit as $\frac{(\cancel{x} - \sqrt{\cancel{x^2}(1+\frac{2}{x^2})})}{\frac{1}{x}}$. As $x$ approaches infinity, $\frac{2}{x^2}$ approaches zero, so we can simplify further to get $\lim_{x 	o \infty} \frac{-2}{x+\sqrt{x^2+2}}$. As the denominator approaches infinity and the numerator approaches a constant (-2), the limit approaches 0. Therefore, the answer is (C).

Evaluate the Limit lim⁡x→∞(x−x2+2)\lim _{x \rightarrow \infty}\left(x-\sqrt{x^{2}+2}\right)limx→∞​(x−x2+2​) A) -2 B) 1 C) 0 D) 2

Evaluate the Limit $\lim _{x \rightarrow \infty}\left(x-\sqrt{x^{2}+2}\right)$ A) -2
B) 1
C) 0
D) 2