Download App

Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
In order that the function $f (x)=(x+1)^{\cot x}$ is continuous at $x=0, f (0)$ must be defined as
  • A
    $f(0)=\frac{1}{e}$
  • B
    $f(0)=0$
  • ✓
    $f(0)=e$
  • D
    $f(0)=e^2$
✓

Answer

Correct option: C.
$f(0)=e$
(C)
For $f (x)$ to be continuous at $x=0$,
$f (0)=\lim _{x \rightarrow 0} f (x)$
$=\lim _{x \rightarrow 0}(x+1)^{\cot x}$
$=\lim _{x \rightarrow 0}\left\{(1+x)^{\frac{1}{x}}\right\}^{x \cot x}$
$=\lim _{x \rightarrow 0}\left\{(1+x)^{\frac{1}{x}}\right\}^{\lim _{x \rightarrow 0}\left(\frac{x}{\tan x}\right)}$
$= e ^1= e$

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 Continuity→Continuity — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $\left|z^2-1\right|=|z|^2+1$, then $z$ lies on
→
The value of the sum $\sum_{n=1}^{13}\left(i^n+i^{n+1}\right)$, where $i=\sqrt{-1}$, equals
→
If ${^\text{20}}\text{C}_{\text{r}}={^\text{20}}\text{C}_{\text{r-10}}$ is then ${^\text{18}}\text{C}_{\text{r}}$ equal to :
→
The distance between the directrices of the ellipse $\frac{x^2}{36}+\frac{y^2}{20}=1$ is
→
Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively, (a, b > 0)
→
$\lim _{x \rightarrow 2}\left(\frac{x^4-16}{x^2-5 x+6}\right)=$
→
Let A = {1, 2, 3} and B = {2, 3, 4} then which of the following is a function from A to B?
→
If ${^\text{m}}\text{C}_{\text{1}}={^\text{n}}\text{C}_{\text{2}},$ is then :
→
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is
→
If the origin is shifted to the point (-3, 2), axes remaining parallel, the new co-ordinate of the point is (3, 1), then its old co-ordinate will be
→