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 $f(x) = \left\{ \begin{array}{l}\frac{{{x^4} - 16}}{{x - 2}},\,\,{\rm{when}}\,\,x \ne 2\\\,\,\,\,\,\,\,\,\,\,\,\,\,16,\,{\rm{when}}\,\,x = 2\end{array} \right.$, then
  • A
    $f(x)$ is continuous at $x = 2$
  • B
    $f(x)$ is discountinous at $x = 2$
  • C
    $\mathop {\lim }\limits_{x \to 2} f(x) = 16$
  • D
    None of these
✓

Answer

$\mathop {\lim }\limits_{x \to 2} \,f(x) = \mathop {\lim }\limits_{x \to 2} \,(x + 2)\,\,({x^2} + 4) = 32,$
$f(2) = 16.$

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 ${A_i} = \left[ {\begin{array}{*{20}{c}}{{a^i}}&{{b^i}}\\{{b^i}}&{{a^i}}\end{array}} \right]$and if $|a|\, < 1,\,|b|\, < 1$, then $\sum\limits_{i = 1}^\infty {\det ({A_i})} $is equal to
→
Let $T_1$ and $T_2$ be two distinct common tangents to the ellipse $E: \frac{x^2}{6}+\frac{y^2}{3}=1$ and the parabola $P: y^2=12 x$. Suppose that the tangent $T_1$ touches $P$ and $E$ at the point $A_1$ and $A_2$, respectively and the tangent $T_2$ touches $P$ and $E$ at the points $A_4$ and $A_3$, respectively. Then which of the following statements is(are) true?

($A$) The area of the quadrilateral $A_1 A _2  A _3 A _4$ is $35$ square units

($B$) The area of the quadrilateral $A_1 A_2 A_3 A_4$ is $36$ square units

($C$) The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-3,0)$

($D$) The tangents $T_1$ and $T_2$ meet the $x$-axis at the point $(-6,0)$

→
If $OA$ and $OB$ be the tangents to the circle ${x^2} + {y^2} - 6x - 8y + 21 = 0$ drawn from the origin $O$, then $AB =$
→
Solve the equations $\left|\begin{array}{ccc}x+a & x & x \\ x & x+a & x \\ x & x & x+a\end{array}\right|=0, a \neq 0$
→
If $x\, = \,{\sin ^{ - 1}}(\sin \,10)$ and $y = \,{\cos ^{ - 1}}\,(\cos \,10)$ , then $y -x$ is equal to
→
If $\sin \theta + \sin \varphi = a$ and $\cos \theta + \cos \phi = b,$ then $\tan \frac{{\theta - \phi }}{2}$ is equal to
→
A seven digit number is formed using digits $3 ,3,4,4,4,5,5 .$ The probability, that number so formed is divisible by $2,$ is ..... .
→
Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that $\frac{|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}|-|\vec{a}-\vec{b}|}=\sqrt{2}+1$. Then $\frac{|\vec{a}+\vec{b}|^{2}}{|\vec{a}|^{2}}$ is :
→
The sum of the solutions of the equation $\left| {\sqrt x  - 2} \right| + \sqrt x \left( {\sqrt x  - 4} \right) + 2 = 0\left( {x > 0} \right)$ is equal to
→
Two parabolas with a common vertex and with axes along $x-$ axis and $y-$ axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is $3$ , then the equation of the common tangent to the two parabolas is?
→