Download App

STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {\lim }\limits_{\alpha \to \beta } \left[ {\frac{{{{\sin }^2}\alpha - {{\sin }^2}\beta }}{{{\alpha ^2} - {\beta ^2}}}} \right] = $
  • A
    $0$
  • B
    $1$
  • C
    $\frac{{\sin \beta }}{\beta }$
  • ✓
    $\frac{{\sin 2\beta }}{{2\beta }}$
✓

Answer

Correct option: D.
$\frac{{\sin 2\beta }}{{2\beta }}$
d
(d) $\mathop {\lim }\limits_{\alpha \to \beta } \frac{{{{\sin }^2}\alpha - {{\sin }^2}\beta }}{{{\alpha ^2} - {\beta ^2}}}$

Applying $ L-$ Hospital’s rule,

$\mathop {{\rm{lim}}}\limits_{\alpha \to \beta } \frac{{2\sin \,\alpha \,\,\cos \alpha }}{{2\alpha }} = \mathop {{\rm{lim}}}\limits_{\alpha \to \beta } \frac{{\sin \,\,2\alpha }}{{2\alpha }} = \frac{{\sin \,\,2\beta }}{{2\beta }}$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Eccentricity of the ellipse $9{x^2} + 25{y^2} = 225$ is
→
The sum of all the local minimum values of the twice differentiable function $\mathrm{F}: \mathrm{R} \rightarrow \mathrm{R}$ defined by $f(x)=x^{3}-3 x^{2}-\frac{3 f^{\prime \prime}(2)}{2} x+f^{\prime \prime}(1)$ is:
→
Exact set of values of $a$ for which ${x^3}(x + 1) = 2(x + a)(x + 2a)$ is having four real solutions is
→
The line $\frac{x}{a} + \frac{y}{b} = 1$ moves in such a way that $\frac{1}{{{a^2}}} + \frac{1}{{{b^2}}} + \frac{1}{{2{c^2}}}$, where $a, b, c \in R_0$ and $c$ is constant, then locus of the foot of the perpendicular from the origin on the given line is -
→
The geometric series $a + ar + ar^2 + ar^3 +..... \infty$ has sum $7$ and the terms involving odd powers of $r$ has sum $'3'$, then the value of $(a^2 -r^2)$ is -
→
The solution of the differential equation $3{e^x}\tan ydx + (1 - {e^x}){\sec ^2}ydy = 0$ is
→
Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$
→
Let $f: \left(-\frac{\pi}{4}, \frac{\pi}{4}\right) \rightarrow \mathrm{R}$ be defined as

$f(x)=(1+|\sin x|)^{\frac{3 a}{\sin x \mid}} ,\quad -\frac{\pi}{4}\,<\,x\,<\,0$

$\quad\quad\quad\quad\quad\quad b ,\quad\quad\quad\quad\quad x=0$

$\quad\quad\quad\quad e^{\cot 4 x / \cot 2 x} ,\quad\quad\quad 0\,<\,x\,<\,\frac{\pi}{4}$

If $\mathrm{f}$ is continuous at $\mathrm{x}=0$, then the value of $6 \mathrm{a}+\mathrm{b}^{2}$ is equal to:

→
If the radius of a circle increases from  $3 \,\, cm$ to  $3.2 \,\, cm,$ then the increase in the area of the circle is
→
If $y = \log \log x$, then ${e^y}{{dy} \over {dx}} = $
→