_ x 0 ( x) - 1 x^2 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0} \frac{{\cos (\sin x) - 1}}{{{x^2}}} = $

A
$1$
B
$-1$
C
$1/2$
✓
$-1/2$

✓

Answer

Correct option: D.

$-1/2$

d
(d) $\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{\cos (\sin x) - 1}}{{{x^2}}}$

$= \mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{ - 2{{\sin }^2}\left( {\frac{{\sin x}}{2}} \right)}}{{{x^2}}} = - 2.\frac{1}{4} = \frac{{ - 1}}{2}$.

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

If ${x^m}{y^n} = {(x + y)^{m + n}}$ then ${\left. {{{dy} \over {dx}}} \right|_{x = 1,y = 2}}$ is equal to

Let $\mathrm{X}=\{\mathrm{n} \in \mathrm{N}: 1 \leq \mathrm{n} \leq 50\} .$ If $A=\{n \in X: n \text { is a multiple of } 2\}$ and $\mathrm{B}=\{\mathrm{n} \in \mathrm{X}: \mathrm{n} \text { is a multiple of } 7\},$ then the number of elements in the smallest subset of $X$ containing both $\mathrm{A}$ and $\mathrm{B}$ is

Let $\overrightarrow{A}=i+j+k$ , $\overrightarrow B = i,\,\overrightarrow C = {C_1}i + {C_2}j + {C_3}k$. If ${C_2} = - 1$, and ${C_3} = 1$, then to make three vectors coplanar

A man walks a distance of $3$ units from the origin towards the north-east $\left(\mathrm{N} 45^{\circ} \mathrm{E}\right)$ direction. From there, he walks a distance of $4$ units towards the north-west $\left(\mathrm{N} 45^{\circ} \mathrm{W}\right)$ direction to reach a point $\mathrm{P}$. Then the position of $\mathrm{P}$ in the Argand plane is

The solution of the differential equation $(\sin x + \cos x)dy + (\cos x - \sin x)dx = 0$ is

$\frac{{\sqrt {1 + \sin x} + \sqrt {1 - \sin x} }}{{\sqrt {1 + \sin x} - \sqrt {1 - \sin x} }} = $ (when $x$ lies in $II^{nd}$ quadrant)

If the system of equation
$2 x+\lambda y+3 z=5$
$3 x+2 y-z=7$
$4 x+5 y+\mu z=9$
has infinitely many solutions, then $\left(\lambda^{2}+\mu^{2}\right)$ is equal to :

Jairam purchased a house in Rs. $15000$ and paid Rs. $5000$ at once. Rest money he promised to pay in annual installment of Rs. $1000$ with $10\%$ per annum interest. How much money is to be paid by Jairam $\mathrm{Rs.}$ ...................

$\mathop \smallint \limits_0^{1.5} x\left[ {{x^2}} \right]dx = $

The total number of two digit numbers $'n',$ such that $3^{n}+7^{n}$ is a multiple of $10 ,$ is ..... .