_ x x x = - Vidyadip

MCQ

$\lim _{x \rightarrow \infty} \frac{\sin x}{x}=$

A
$2$
B
$1$
C
$\infty$
✓
$0$

✓

Answer

Correct option: D.

$0$

Explanation: $\lim _{x \rightarrow \infty} \frac{\sin x}{x}$
$\text { Let } x=\frac{1}{y}$
$x \rightarrow \infty$
$\therefore y \rightarrow 0$
$=\underset{{y \rightarrow 0}}{\lim} \frac{\sin \frac{1}{y}}{\frac{1}{y}}$
$=\underset{{y \rightarrow 0}}{\lim} y \sin \frac{1}{y}$
$=\underset{{y \rightarrow 0}}{\lim} y \times \underset{{y \rightarrow 0}}{\lim} \sin \frac{1}{y}$
$=0 \times \underset{{y \rightarrow 0}}{\lim} \sin \frac{1}{y}$
$=0$

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 "M.C.Q (1 Marks)" from Model Paper 7→Model Paper 7 — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The line $3x - 4y = 5$ is a tangent to the hyperbola ${x^2} - 4{y^2} = 5$. The point of contact is

If $\text{x}\sin45^\circ\cos^260^\circ=\frac{\tan^260^\circ\text{cosec }30^\circ}{\sec45^\circ\cot^230^\circ},$ then x =

The tangent at $P$, any point on the circle ${x^2} + {y^2} = 4$, meets the coordinate axes in $A$ and $B$, then

For the equation $|x|^2+|x|-6=0$, the sum of the real roots is:

Let $\alpha, \beta$ be the roots of the equation $x^2-\sqrt{6} x+3=0$ such that $\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)$. Let $a, b$ be integers not divisible by $3$ and $n$ be a natural number such that $\frac{\alpha^{99}}{\beta}+\alpha^{98}=3^n(a+i b), i=\sqrt{-1}$. Then $\mathrm{n}+\mathrm{a}+\mathrm{b}$ is equal to_.....................

If $aN = \{ ax:x \in N\} ,$ then the set $3N \cap 7N$ is .....$N$

If the circles $x^2 + y^2 + 2ax + c = 0$ and $x^2 + y^2 + 2by + c = 0$ touch each other, then:

If $2$ and $6$ are the roots of the equation $a x^2+b x+1=0$, then the quadratic equation, whose roots are $\frac{1}{2 a+b}$ and $\frac{1}{6 a+b}$, is :

The smallest possible positive slope of a line whose $y$-intercept is $5$ and which has a common point with the ellipse $9 x^2+16 y^2=144$ is

The straight lines $4ax + 3by + c = 0$ where $a + b + c = 0$, will be concurrent, if point is