Download App

STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If $f(x) = \left\{ \begin{array}{l}\frac{1}{x}\sin {x^2},\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,x = 0\end{array} \right.$, then
  • A
    $\mathop {\lim }\limits_{x \to 0 + } f(x) \ne 0$
  • B
    $\mathop {\lim }\limits_{x \to 0 - } f(x) \ne 0$
  • C
    $f(x),$ is continuous at $x = 0 $
  • D
    None of these
✓

Answer

$f(0) = 0,\,\mathop {\lim }\limits_{x \to 0 + } f(x) = \mathop {\lim }\limits_{x \to 0 - } f(x) = \mathop {\lim }\limits_{x \to 0} \,x\,\left[ {\frac{{\sin {x^2}}}{{{x^2}}}} \right] = 0$.

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

If the value of $\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}$ is $\frac{a \sqrt{5}-b}{c}, $ where $a, b, c$ are natural numbers and $\text{gcd} (a, c) = 1,$ then $a + b + c$ is equal to:
→
The latus rectum of the hyperbola $9{x^2} - 16{y^2} - 18x - 32y - 151 = 0$ is
→
Let $a_1, a_2, a_3, \ldots$ be an arithmetic progression with $a_1=7$ and common difference $8$ . Let $T_1, T_2, T_3, \ldots$ be such that $T_1=3$ and $T_{n+1}-T_n=a_n$ for $n \geq 1$. Then, which of the following is/are $TRUE$ ?

$(A)$ $T_{20}=1604$

$(B)$ $\sum_{ k =1}^{20} T_{ k }=10510$

$(C)$ $T_{30}=3454$

$(D)$ $\sum_{ k =1}^{30} T_{ k }=35610$

→
Let $f:\left( { - 1,1} \right) \to R$ be differentiable function with $f\left( 0 \right) = - 1$ and $f'\left( 0 \right) = 1$ . Let $g\left( x \right) = {\left[ {f\left( {2f\left( x \right) + 2} \right)} \right]^2}$ .Then $g'\left( 0 \right) = $
→
Let the solution curve $y = y ( x )$ of the differential equation $\quad \frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{\frac{3}{2}}} y=2 x$ $\exp \frac{x^3-\tan ^{-1} x^3}{\sqrt{(1+x)^6}}$ pass through the origin. Then $y (1)$ is equal to:
→
The equation $\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} $ has
→
Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is
→
If the geometric mean between $a$ and $b$ is $\frac{{{a^{n + 1}} + {b^{n + 1}}}}{{{a^n} + {b^n}}}$, then the value of $n$ is
→
Period of $\cot 3x - \cos (4x + 3)$ is
→
If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :
→