Evaluate: _ x 0 x+ x x- - Vidyadip

MCQ

Evaluate: $ \displaystyle \lim_{\text{x}\rightarrow 0}\frac{\sin \text{x}+\cos \text{x}}{\sin \text{x}-\cos\text{x}}$

A
$0$
B
$1$
✓
$-1$
D
$\infty $

✓

Answer

Correct option: C.

$-1$

$ \displaystyle \lim_{\text{x}\rightarrow 0}\frac{\sin \text{x}+\cos \text{x}}{\sin \text{x}-\cos\text{x}}$
Substituting $x = 0,$ we get
$= \displaystyle \lim_{\text{x}\rightarrow 0}\frac{\sin \text{x}+\cos \text{x}}{\sin \text{x}-\cos\text{x}}$
$= \displaystyle \lim_{\text{x}\rightarrow 0}\frac{\sin \text{0}+\cos \text{0}}{\sin \text{0}-\cos\text{0}}$
$ = \displaystyle \lim_{\text{x}\rightarrow 0}\frac{\ \text{0}+\text{1}}{0-1}$

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