_ x 0 7 x 11 x 5 x^2 = - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{\sin 7 x \cdot \sin 11 x}{5 x^2}=$

A
$\frac{89}{5}$
B
$\frac{56}{3}$
✓
$\frac{77}{5}$
D
$\frac{65}{3}$

✓

Answer

Correct option: C.

$\frac{77}{5}$

(C)
$\lim _{x \rightarrow 0} \frac{\sin 7 x \cdot \sin 11 x}{5 x^2}$
$=\frac{1}{5} \lim _{x \rightarrow 0} \frac{\sin 7 x}{x} \times \lim _{x \rightarrow 0} \frac{\sin 11 x}{x}$
$=\frac{1}{5} \lim _{x \rightarrow 0} \frac{\sin 7 x}{7 x} \times 7 \times \lim _{x \rightarrow 0} \frac{\sin 11 x}{11 x} \times 11$
$=\frac{1}{5} \times 7 \times 11$
$=\frac{77}{5}$

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 "MCQ" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the straight line $x \cos \alpha+y \sin \alpha= p$ be a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, then

If vertices of a parallelogram are respectively (0, 0), (1, 0), (2, 2) and (1, 2), then angle between diagonals is

The area of the circle having centre at (1, 2) and passing through (4, 6) is

If the coordinates of the vertex and the focus of a parabola are $(-1, 1)$ and $(2, 3) $respectively, then the equation of its directrix is

Maximum and minimum values of $\sin ^4 \theta+\cos ^4 \theta$ are

In how many ways can a committee of $5$ be made out of $6$ men and $4$ women containing at least one women?

The auxiliary equation of circle of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, is

Consider the circle $x^2+y^2-6 x+4 y=12$. The equation of a tangent to this circle that is parallel to the line $4 x+3 y+5=0$ is

$\frac{\sin5\text{x}}{\sin\text{x}}$ is equal to :

General solution of $\tan5\text{x}=\cot2\text{x}$ is :