MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{3\sin x - \sin 3x}}{{{x^3}}} = $
  • $4$
  • B
    $-4$
  • C
    $\frac{1}{4}$
  • D
    None of these

Answer

Correct option: A.
$4$
a
(a) $\mathop {\lim }\limits_{x \to 0} \,\,\frac{{4\,{{\sin }^3}x}}{{{x^3}}} = 4.$

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

Similar questions

The minimum value of the expression $|z|+|z-1|+|z-1-i|+|z-i|$, where $z$ is a complex number and $i=\sqrt{-1}$, is
There are $15$ persons in a party and each person shake hand with another, then total number of hand shakes is
Sum of first $n$ terms in the following series ${\cot ^{ - 1}}3 + {\cot ^{ - 1}}7 + {\cot ^{ - 1}}13 + {\cot ^{ - 1}}21 + .............$ is given by
The smallest natural number $n,$ such that the coefficient of $x$ in the expansion of ${\left( {{x^2}\, + \,\frac{1}{{{x^3}}}} \right)^n}$ is $^n{C_{23}}$ is
The tangent drawn at any point $P$ to the parabola ${y^2} = 4ax$ meets the directrix at the point $K$, then the angle which $KP$ subtends at its focus is ............. $^\circ$
If $0<\theta, \phi<\frac{\pi}{2}, x =\sum_{ n =0}^{\infty} \cos ^{2 n } \theta, y =\sum_{ n =0}^{\infty} \sin ^{2 n } \phi$ and $z =\sum_{ n =0}^{\infty} \cos ^{2 n } \theta \cdot \sin ^{2 n } \phi$ then
For three events $A,B $ and $C$  ,$P ($ Exactly one of $A$ or $B$ occurs$)\, =\, P ($ Exactly one of $C$ or $A$ occurs $) =$ $\frac{1}{4}$ and $P ($ All the three events occur simultaneously $) =$ $\frac{1}{16}$ Then the probability that at least one of the events occurs is :
The range of values of $'a'$ such that the angle $\theta$ between the pair of tangents drawn from the point $(a, 0)$ to the circle $x^2 + y^2 = 1$ satisfies $\frac{\pi }{2} < \theta < \pi$ is :
The equation of the parabola with $(-3, 0)$ as focus and $x + 5 = 0$ as directirx, is
If pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is: