_ x 0 e^ 2 | sin x | -2| x|-1 x^2 - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{e^{2 |\text { sin } x | \mid}-2|\sin x|-1}{x^2}$

A
is equal to -$1$
B
does not exist
C
is equal to $1$
✓
is equal to $2$

✓

Answer

Correct option: D.

is equal to $2$

d
$\lim _{x \rightarrow 0} \frac{e^{2 s i n x}-2|\sin x|-1}{x^2}$

$lim _{x \rightarrow 0} \frac{e^{2 s i n x}-2|\sin x|-1}{|\sin x|^2} \times \frac{\sin ^2 x}{x^2}$

Let $|\sin x|=t$

$\lim _{t \rightarrow 0} \frac{e^{2 t}-2 t-1}{t^2} \times \lim _{x \rightarrow 0} \frac{\sin ^2 x}{x^2}$

$=\lim _{t \rightarrow 0} \frac{2 e^{2 t}-2}{2 t} \times 1=2 \times 1=2$

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

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

Similar questions

Number of real values of $\lambda$ for which the matrix $A =$ $\left[ {\begin{array}{*{20}{c}}{\lambda - 1}&\lambda &{\lambda + 1}\\2&{ - 1}&3\\ {\lambda + 3}&{\lambda - 2}&{\lambda + 7}\end{array}} \right]$ has no inverse

Let $f$ be a differentiable function in $\left(0, \frac{\pi}{2}\right)$ If $\int\limits_{\cos x}^{1} t^{2} f(t) d t=\sin ^{3} x+\cos x-1$ then $\frac{1}{\sqrt{3}} f^{\prime}\left(\frac{1}{\sqrt{3}}\right)$ is equal to

Let $f$ be a differentiable function and equation of normal to the graph of $y = f(x)$ at $x = 3$ is $3y = x + 18$ . If $L\, = \,\mathop {Lim}\limits_{x \to 1} \frac{{f\left( {3 + {{\left( {4{{\tan }^{ - 1}}x - \pi } \right)}^2}} \right) - f\left( {3 + {{\left( {f\left( 3 \right) - x - 6} \right)}^2}} \right)}}{{{{\sin }^2}\left( {x - 1} \right)}}$ then

Value of the definite integral $\int\limits_{ - 1/2}^{1/2}$$( sin^{-1}(3x- 4x^3)- cos^{-1}(4x^3- 3x) )dx$

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 + x}&1\\1&1&{1 + y}\end{array}\,} \right| = $

Number of straight lines that can be drawn from $(2, 5)$ which make a triangle of area $24sq.$ units with the coordinate axes is

$\int {\frac{{dx}}{{{{({a^2} + {x^2})}^{3/2}}}}} $ is equal to

If ${p^{th}},\;{q^{th}},\;{r^{th}}$ and ${s^{th}}$ terms of an $A.P.$ be in $G.P.$, then $(p - q),\;(q - r),\;(r - s)$ will be in

If $a=i+j$ and $b=2i-k$ are two vectors, then the point of intersection of two lines $r \times a = b \times a$ and $r \times a = a \times b$ is

Area bounded by parabola ${y^2} = x$ and straight line $2y = x$ is