_ x 0 x ( e ^ x -1 ) 1- x is equal to - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{x\left( e ^{\sin x}-1\right)}{1-\cos x}$ is equal to

A
1
B
$0$
✓
2
D
$\frac{1}{2}$

✓

Answer

Correct option: C.

2

(C)
$\lim _{x \rightarrow 0} \frac{x\left( e ^{\sin x}-1\right)}{1-\cos x}=\lim _{x \rightarrow 0} \frac{\frac{ e ^{\sin x}-1}{x}}{\frac{1-\cos x}{x^2}}$
$=\left(\lim _{x \rightarrow 0} \frac{ e ^{\sin x}-1}{\sin x} \cdot \frac{\sin x}{x}\right) \times 2=2$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\lim _{x \rightarrow-2}\left(\frac{x^7+128}{x^3+8}\right)=$

An investigator interviewed $100$ students to determine the performance of three drinks: milk, coffee and tea. The investigator reported that $10$ students take all three drinks milk, coffee and tea; $20$ students take milk and coffee; $25$ students take milk and tea; $12$ students take milk only; $5$ students take coffee only and $8$ students take tea only. Then the number of students who did not take any of three drinks is :

If in greatest integer function, the domain is a set of real numbers, then range will be set of

If $\text{y}=1+\frac{\text{x}}{1!}+\frac{\text{x}^2}{2!}+\frac{\text{x}^3}{3!}+\dots,$ then $\frac{\text{dy}}{\text{dx}}=$

Length of intercept on X axis of the locus $x^2+y^2-4 x-6 y-12=0$ is

If $z_1=\sqrt{2}\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)$ and $z_2=\sqrt{3}\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)$, then $\left|z_1 z_2\right|$ is

If $\theta=60^{\circ}$, then $\frac{1+\tan ^2 \theta}{2 \tan \theta}$ is equal to

$\lim _{x \rightarrow a} \frac{\cos x-\cos a}{\cot x-\cot a}=$

If $\cos (\theta-\alpha)=a, \sin (\theta-\beta)=b$, then $\cos ^2(\alpha-\beta)+2 ab \ \sin (\alpha-\beta)$ is equal to

The value of $\lim _{x \rightarrow 0} \frac{\left(4^{\prime}-1\right)^3}{\sin \frac{x^2}{4} \log (1+3 x)}$ is