Download App

STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}{(1 + 2x)^{1/x}},\,{\rm{for\,\, }}x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{e^2},\,{\rm{for\,\, }}x = 0\,\,\,\end{array} \right.$, then
  • A
    $\mathop {\lim }\limits_{x \to 0 + } f(x) = e$
  • ✓
    $\mathop {\lim }\limits_{x \to 0 - } f(x) = {e^2}$
  • C
    $f(x)$ is discontinuous at $x = 0$
  • D
    None of these
✓

Answer

Correct option: B.
$\mathop {\lim }\limits_{x \to 0 - } f(x) = {e^2}$
b
(b) $\mathop {\lim }\limits_{x \to 0 - } f(x) = \mathop {\lim }\limits_{x \to 0} \,\,{\left[ {{{(1 + 2x)}^{1/2x}}} \right]^2} = {e^2}.$

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 STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $A=\left[\begin{array}{cc}1+2 i & i \\ -i & 1-2 i\end{array}\right]$, where $i=\sqrt{-1}$, then $A(\operatorname{adj} A)=$
→
Let A = {1, 2, 3}. Then the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive is:
→
The area bounded by the curve $y^2=8 x,$ the $x-$ axis and the lastus rectum is :
→
The number of arbitrary constants in the particular solution of differential equation of fourth order is:
→
Choose the correct answer from given four options in each of the Exercise : The number of distinct real roots of $\begin{vmatrix}\sin\text{x}&\cos\text{x}&\cos\text{x}\\\cos\text{x}&\sin\text{x}&\cos\text{x}\\\cos\text{x}&\cos\text{x}&\sin\text{x}\end{vmatrix}=0$ in the interval $-\frac{\pi}{4}\leq\text{x}\leq\frac{\pi}{4}$ is:
→
${d \over {dx}}({e^x}\log \sin 2x) = $
→
Let $f\left( x \right) = x\left| x \right|\,,\,g\left( x \right) = \sin \,x$ and $h\left( x \right) = \left( {gof} \right)\left( x \right)$. Then
→
Let $ S = \{t \in R : f(x)= |x-\pi|.(e^{|x|}-1)sin|x|$ is not differentiable at $t\,\,\}$. Then the set $S$ is equal to :
→
The relation S defined on the set R of all real number by the rule aSb iff a ≥ b is:
→
If for the matrix $A, A^3 = I,$ than $A^{-1} =$
→