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) $\mathop {\lim }\limits_{x \to \alpha } \,\,\frac{{\sin x - \sin \alpha }}{{x - \alpha }}$
(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.
Explore more
Similar questions
$\int_{}^{} {\frac{{{{\sin }^3}x + {{\cos }^3}x}}{{{{\sin }^2}x{{\cos }^2}x}}} \;dx = $
→Two vertices of a triangle are $(5,4)$ and $(-2,4)$. If its centroid is $(5,6)$ then the third vertex has the coordinates
→Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is
If $y = \sin \left( {{{1 + {x^2}} \over {1 - {x^2}}}} \right)$, then ${{dy} \over {dx}} = $
→The shortest distance between the lines ${r_1} = 4i - 3j - k + \lambda (i - 4j + 7k)$ and ${r_2} = i - j - 10k + \lambda (2i - 3j + 8k)$ is
→Let $y = {t^{10}} + 1$ and $x = {t^8} + 1,$ then ${{{d^2}y} \over {d{x^2}}}$ is
→An online exam is attempted by $50$ candidates out of which $20$ are boys. The average marks obtained by boys is $12$ with a variance $2 .$ The variance of marks obtained by $30$ girls is also $2 .$ The average marks of all $50$ candidates is $15 .$ If $\mu$ is the average marks of girls and $\sigma^{2}$ is the variance of marks of $50$ candidates, then $\mu+\sigma^{2}$ is equal to ...... .
→Six $‘X'$ s have to be placed in the square of the figure such that each row contains at least one $X$. In how many different ways can this be done
→Let $f(x) = \left\{ \begin{array}{l}{x^p}\sin \frac{1}{x},x \ne 0\\0\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x = 0\end{array} \right.$ then $f(x)$ is continuous but not differential at $x = 0$ if
→Integrating factor of the differential equation $\frac{{dy}}{{dx}} + y\tan x - \sec x = 0$ is
→