Download App

5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $f(x)=\left\{\begin{array}{cl}x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$, then
  • A
    $f^{\prime \prime}(0)=1$
  • ✓
    $\mathrm{f}^{\prime \prime}\left(\frac{2}{\pi}\right)=\frac{24-\pi^2}{2 \pi}$
  • C
    $f^{\prime \prime}\left(\frac{2}{\pi}\right)=\frac{12-\pi^2}{2 \pi}$
  • D
    $f^{\prime \prime}(0)=0$
✓

Answer

Correct option: B.
$\mathrm{f}^{\prime \prime}\left(\frac{2}{\pi}\right)=\frac{24-\pi^2}{2 \pi}$
b
$ f^{\prime}(x)=3 x^2 \sin \left(\frac{1}{x}\right)-x \cos \left(\frac{1}{x}\right) $

$ f^{\prime \prime}(x)=6 x \sin \left(\frac{1}{x}\right)-3 \cos \left(\frac{1}{x}\right)-\cos \left(\frac{1}{x}\right)-\frac{\sin \left(\frac{1}{x}\right)}{x} $

$ f^{\prime \prime}\left(\frac{2}{\pi}\right)=\frac{12}{\pi}-\frac{\pi}{2}=\frac{24-\pi^2}{2 \pi}$

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 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The matrix $\left[ {\begin{array}{*{20}{c}}0&5&{ - 7}\\{ - 5}&0&{11}\\7&{ - 11}&0\end{array}} \right]$is known as
→
Maximum value of $x{(1 - x)^2}$ when $0 \le x \le 2$, is
→
Let $O$ be the origin and $\overline{ OA }=2 \hat{ i }+2 \hat{ j }+\hat{ k }, \overline{ OB }=\hat{ i }-2 \hat{ j }+2 \hat{ k }$ and $\overline{ OC }=\frac{1}{2}(\overline{ OB }-\lambda \overline{ OA })$ for some $\lambda>0$. If $|\overline{ OB } \times \overline{ OC }|=\frac{9}{2}$, then which of the following statements is (are) TRUE?

$(A)$ Projection of $\overline{ OC }$ on $\overline{ OA }$ is $-\frac{3}{2}$

$(B)$ Area of the triangle $OAB$ is $\frac{9}{2}$

$(C)$ Area of the triangle $ABC$ is $\frac{9}{2}$

$(D)$ The acute angle between the diagonals of the parallelogram with adjacent sides $\overline{ OA }$ and $\overline{ OC }$ is $\frac{\pi}{3}$

→
If the system of equations

$ x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 $

$ x+(\cos \alpha) y+(\sin \alpha) z=0 $

$ x+(\sin \alpha) y-(\cos \alpha) z=0$

has a non-trivial solution, then $\alpha \in\left(0, \frac{\pi}{2}\right)$ is equal to :

→
Z = 4x1 + 5x2, subject to $2\text{x}_{1}+\text{x}_{2}\geq7,2\text{x}_{1}+3\text{x}2\leq15,\text{x}_{2}\leq3,\text{x}_{1},\text{x}_{2}\geq0.$ The minimum value of Z occurs at:
→
If $[x]$ is the greatest integer $ \leq x$, then the value of the integral $\int\limits_{ - 0.9}^{0.9} {\left( {\left[ {{x^2}} \right] + \log \left( {\frac{{2 - x}}{{2 + x}}} \right)} \right)} dx$ is
→
$\int \frac{d x}{e^x+e^{-x}}=$ _________ + C.
→
If ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{{2\pi }}{3},$ then ${\cos ^{ - 1}}x + {\cos ^{ - 1}}y = $
→
Point (4, 0) lies on ________?
  1. $\vec{\text{XO}}$
  2. $\vec{\text{YO}}$
  3. $\vec{\text{OX}}$
  4. $\vec{\text{OY}}$
→
If $f(x) = g(x)$, then the value of $\int_{}^{} {f'(x)} \;.\;g(x)\;dx$ is
→