limx→0(x+2sinx)/(√(x^2+2 sin x+1) - √(sin^2x-x+1)) is

Correct answer: (C) 2. limx→0(x+2sinx)/(√(x^2+2sinx+1)−√(sinx−x+1)) 0/0form By using L'Hospital Rule, =limx→0(1+2cosx)/(12x+2cosx2√(x^2+2sinx+1))−(1sin2x−1)/(2√(sin^2x−x+1)) =(1+2)/(1+12)=3/32=2.

Q36 / 90 · JEE Main 2019 (12 Apr Shift 2) · Mathematics

$\underset{x \to 0}{l i m} \frac{x + 2 s i n x}{\sqrt{x^{2} + 2 s i n x + 1} - \sqrt{{s i n}^{2} x - x + 1}}$ is

A
$3$
B
$1$
Correct answer
C
$2$
D
$6$

Solution

$\lim_{x \to 0} \frac{x + 2 \sin x}{\sqrt{x^{2} + 2 \sin x + 1} - \sqrt{\sin x - x + 1}}$ $(\frac{0}{0} form)$

By using L'Hospital Rule,

$= \lim_{x \to 0} \frac{1 + 2 \cos x}{\frac{1 (2 x + 2 \cos x)}{2 \sqrt{x^{2} + 2 \sin x + 1}} - \frac{1 (\sin 2 x - 1)}{2 \sqrt{\sin^{2} x - x + 1}}}$

$= \frac{1 + 2}{1 + \frac{1}{2}} = \frac{3}{\frac{3}{2}} = 2$ .

Hence, the correct answer is option: 'C'.

limx→0x+2sinxx2+2 sin x+1 - sin2x-x+1 is

Solution

Relevant Questions

$\underset{x \to 0}{l i m} \frac{x + 2 s i n x}{\sqrt{x^{2} + 2 s i n x + 1} - \sqrt{{s i n}^{2} x - x + 1}}$ is