_ x 0 5 x + x x 2 x - x^2 is - Vidyadip

Question

$\mathop {\lim }\limits_{x \to 0} \frac{{5\sin x + x\cos x}}{{2\tan x - {x^2}}}$ is

✓

Answer

b
$\mathop {\lim }\limits_{x \to 0} \frac{{5\sin x + x\cos x}}{{2\tan x - {x^2}}}$

$\mathop {\lim }\limits_{x \to 0} \frac{{5\frac{{\sin x}}{x} + \cos x}}{{\frac{{2\tan x}}{x} - x}} = \frac{{5 + 1}}{{2 - 0}} = 3$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\mathop {\lim }\limits_{x \to 0} {x^x} = $

The area bounded by the curves $y = \,|x| - 1$ and $y = - |x| + 1$ is

The sum of the coefficients in the expansion of ${(1 + x - 3{x^2})^{3148}}$ is

If ${\tan ^{ - 1}}x + {\tan ^{ - 1}}y + {\tan ^{ - 1}}z = \pi ,$ then $\frac{1}{{xy}} + \frac{1}{{yz}} + \frac{1}{{zx}} = $

Let $\vec{a}=2 \hat{i}-\hat{j}+5 \hat{k}$ and $\vec{b}=\alpha \hat{i}+\beta \hat{j}+2 \hat{k}$. If $((\vec{a} \times \vec{b}) \times \hat{i}) \cdot \hat{k}=\frac{23}{2}$, then $|\vec{b} \times 2 \hat{j}|$ is equal to.

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+5\, \hat{\mathrm{j}}+\alpha\, \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+3 \,\hat{\mathrm{j}}+\beta\, \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=-\hat{\mathrm{i}}+2\, \hat{\mathrm{j}}-3 \,\hat{\mathrm{k}}$ be three vectors such that, $|\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}|=5 \sqrt{3}$ and $\overrightarrow{\mathrm{a}}$ is perpendicular to $\overrightarrow{\mathrm{b}}$. Then the greatest amongst the values of $|\vec{a}|^{2}$ is .... .

Suppose the sequence $a_1, a_2, a_3, \ldots$ is a n arithmetic progression of distinct numbers such that the sequence $a_1, a_2, a_4, a_8, \ldots$ is a geometric progression. The common ratio of the geometric progression is

Let $a_1 , a_2, a_3, .... , a_n,$ be in $A.P$. If $a_3 + a_7 + a_{11} + a_{15} = 72$ , then the sum of its first $17$ terms is equal to

Suppose $\quad f : R \rightarrow(0, \infty)$ be a differentiable function such that $5 f ( x + y )= f ( x ) \cdot f ( y ), \forall x , y \in R$. If $f(3)=320$, then $\sum \limits_{n=0}^5 f(n)$ is equal to :

If $f(3) = 6 \& f ‘ (3) = 2$, then $\mathop {Limit}\limits_{x\,\, \to \,\,3} $ $\frac{{x\,f(3)\,\, - \,\,3\,f\,(x)}}{{x\,\, - \,\,3}}$ is given by :