_ x x x = - Vidyadip

MCQ

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

A
2
B
1
C
$\infty$
D
$0$

✓

Answer

(d) 0
Explanation: $\lim _{x \rightarrow \infty} \frac{\sin x}{x}$
$\begin{array}{l}\text { Let } x=\frac{1}{y} \\ x \rightarrow \infty \\ \therefore y \rightarrow 0\end{array}$
$\begin{array}{l}=\underset{{y \rightarrow 0}}{\lim} \frac{\sin \frac{1}{y}}{\frac{1}{y}} \\ =\underset{{y \rightarrow 0}}{\lim} y \sin \frac{1}{y} \\ =\underset{{y \rightarrow 0}}{\lim} y \times \underset{{y \rightarrow 0}}{\lim} \sin \frac{1}{y} \\ =0 \times \underset{{y \rightarrow 0}}{\lim} \sin \frac{1}{y} \\ =0\end{array}$

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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\tan\text{x}+\sec\text{x}=\sqrt{3},0<\text{x}<\pi,$ then x is equal to:

$\frac{5\pi}{6}$
$\frac{2\pi}{3}$
$\frac{\pi}{6}$
$\frac{\pi}{3}$

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing exactly two elements is:

Let A and B be two sets in the same universal set. Then, A - B =

If A and B are two disjoint sets, then $\text{n(A}\cup\text{B)}$ is equal to:

$\text{n(A) + n(B)}$
$\text{n(A) + n(B)} - \text{n(A}\cap\text{B)}$
$\text{n(A) + n(B) + n(A}\cap\text{B)}$
$\text{n(A) n(B)}.$

The probability that the sum of the numbers obtained on throwing two dice simultaneously is a multiple of 4 is :

Area of the triangle formed by the points ((a + 3)(a + 4), a + 3), ((a + 2)(a + 3), (a + 2)) and ((a + 1)(a + 2), (a + 1)) is:

25a²
5a²
24a²
None of these.

Evaluate $\lim _{x \rightarrow 0} \frac{x^2-2 x}{2 \sin x}$ :

If the sum of the roots of the quadratic equation $ \text{ax}^2+\text{bx}+\text{c}=0$ is equal to the sum of the squares of their reciprocals, then $\frac{\text{a}}{\text{c}}, \frac{\text{b}}{\text{a}}$ and $\frac{\text{c}}{\text{b}}$ are in:

IF R = {(2, 1), (4, 3), (4, 5)}, then range of the function is?

Equation of line parallel to $3 x-4 y=7$ and passing through origin $(0,0)$ is given by :