_ x x - x - = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to \alpha } \frac{{\sin x - \sin \alpha }}{{x - \alpha }} = $

A
$0$
B
$1$
C
$\sin \alpha $
✓
$\cos \alpha $

✓

Answer

Correct option: D.

$\cos \alpha $

d
(d) $\mathop {\lim }\limits_{x \to \alpha } \,\,\frac{{\sin x - \sin \alpha }}{{x - \alpha }}$

$\mathop {\lim }\limits_{x \to \alpha } \,\,\frac{{\cos x}}{1} = \cos \alpha $, (Apply $L-$Hospital's rule)

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 STD 11 - 12. limits→STD 11 - 12. limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Consider the set $A_n$ of points $(x, y)$ such that $0 \leq x \leq n, 0 y \leq n$ where $n, x, y$ are integers. Let $S_n$ be the set of all lines passing through at least two distinct points from $A_n$. Suppose we choose a line $l$ at random from $S_n$. Let $P_n$ be the probability that $l$ is tangent to the circle $x^2+y^2=n^2\left(1+\left(1-\frac{1}{\sqrt{n}}\right)^2\right)$ Then, the limit $\lim _{n \rightarrow \infty} P_n$ is

A bag contains $3$ white and $7$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

The polar form of $(\text{i}^{25})^3$ is:

If $P(A \cup B) = 0.8$ and $P(A \cap B) = 0.3,$ then $P(\bar A) + P(\bar B) = $

If the intercept made by the line between the axis is bisected at the point $(5, 2)$, then its equation is

The line $12 x \,\cos \theta+5 y \,\sin \theta=60$ is tangent to which of the following curves?

Arranging people, digits, numbers, alphabets, letters, and colours are example of:

Suppose that $x$ and $y$ are positive number with $xy = \frac{1}{9};\,x\left( {y + 1} \right) = \frac{7}{9};\,y\left( {x + 1} \right) = \frac{5}{{18}}$ . The value of $(x + 1) (y + 1)$ equals

If $A = \{1, 2, 3, 4, 5, 6\}, B = \{2, 4, 6, 8\},$ then $A - B$ will be:

Consider the parabola with vertex $\left(\frac{1}{2}, \frac{3}{4}\right)$ and the directrix $\mathrm{y}=\frac{1}{2}$. Let $\mathrm{P}$ be the point where the parabola meets the line $\mathrm{x}=-\frac{1}{2}$. If the normal to the parabola at $\mathrm{P}$ intersects the parabola again at the point $\mathrm{Q}$, then $(\mathrm{PQ})^{2}$ is equal to :