Download App

12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{{2^x} - 1}}{{{{(1 + x)}^{1/2}} - 1}} = $
  • A
    $\log 2$
  • ✓
    $\log 4$
  • C
    $\log \sqrt 2 $
  • D
    None of these
✓

Answer

Correct option: B.
$\log 4$
b
(b) $\mathop {\lim }\limits_{x \to 0} \,\frac{{{2^x} - 1}}{{{{(1 + x)}^{1/2}} - 1}} = \mathop {\lim }\limits_{x \to 0} \,\frac{{{2^x}\log 2}}{{{\textstyle{1 \over 2}}\,{{(1 + x)}^{ - 1/2}}}}$

$\left\{ \because \,\,\,\mathop {\lim }\limits_{x \to a} \,\,\frac{f(x)}{g(x)}=\mathop {\lim }\limits_{x \to a} \,\,\frac{{f}'(x)}{{g}'(x)} \right\}$

$ = 2\,\log 2 = \log 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

Explore more

More "MCQ" from 12. limits→12. limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The number of $5$ digit telephone numbers having at least one of their digits repeated is
→
If in an A.P., first term is 20, common difference is 2 and $n^{th}$ term is 42, then find sum up to n terms.
→
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is:
→
If $\tan\text{A}=\frac{\text{a}}{\text{a}+1}$ and $\text{B}=\frac{1}{2\text{a}+1},$ then the value of A + B is:
→
Let $E_1$ and $E_2$ be two ellipses whose centers are at the origin. The major axes of $E_1$ and $E_2$ lie along the $x$-axis and the $y$-axis, respectively. Let $S$ be the circle $x^2+(y-1)^2=2$. The straight line $x+y=3$ touches the curves $S, E_1$ ad $E_2$ at $P, Q$ and $R$, respectively. Suppose that $P Q=P R=\frac{2 \sqrt{2}}{3}$. If $e_1$ and $e_2$ are the eccentricities of $E_1$ and $E_2$, respectively, then the correct expression$(s)$ is(are)

$(A)$ $e_1^2+e_2^2=\frac{43}{40}$

$(B)$ $e_1 e_2=\frac{\sqrt{7}}{2 \sqrt{10}}$

$(C)$ $\left|e_1^2-e_2^2\right|=\frac{5}{8}$

$(D)$ $e_1 e_2=\frac{\sqrt{3}}{4}$

→
The sum of the series $\left( {\begin{array}{*{20}{c}}{20}\\0\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\1\end{array}} \right)$$+$$\left( {\begin{array}{*{20}{c}}{20}\\2\end{array}} \right) - \left( {\begin{array}{*{20}{c}}{20}\\3\end{array}} \right)$$+…..-……+$$\left( {\begin{array}{*{20}{c}}{20}\\{10}\end{array}} \right)$ 
→
In the $\Delta \text{ABC}$ A = (1, 3, -2) and G (-1, 4, 2) is the centroid of the triangle. If D is the mid point of BC then AD =
→
A quadratic polynomial $ y = f (x)$  with absolute term  $3$  neither touches nor intersects the abscissa axis and is symmetric about the line $x = 1$ . The coefficient of the leading term of the polynomial is unity. A point $A(x_1, y_1)$  with abscissa $x_1 = 1$  and a point $B(x_2, y_2) $ with ordinate $y_2 = 11 $ are given in a cartisian rectangular system of co-ordinates $OXY $ in the first quadrant on the curve $y = f (x)$  where $ 'O'$  is the origin. The graph of $y = f(x)$ represents a parabola whose focus has the co-ordinates
→
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
→
Out of $6$ books, in how many ways can a set of one or more books be chosen
→