Download App

Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0}(1-a x)^{\frac{1}{x}}=$
  • A
    e
  • ✓
    $e ^-a$
  • C
    1
  • D
    $e ^2$
✓

Answer

Correct option: B.
$e ^-a$
(B)
$\lim _{x \rightarrow 0}(1- a x)^{\frac{1}{x}}=\lim _{x \rightarrow 0}\left\{[1+(- a x)]^{\frac{1}{-\frac{1}{2 x}}}\right\}^{-8}$
$= e ^{- a } \quad \ldots .\left[\because \lim (1+x)^{\frac{1}{x}}= e \right]$

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

Similar questions

Let $S , T , U$ be three non-void sets and $f : S \rightarrow T$, $g : T \rightarrow U$ be so that g of $: S \rightarrow U$ is surjective. Then
→
If the domain of function $f ( x )=x^2-6 x+7$ is $(-\infty, \infty)$, then the range of function is
→
$1+\cos 10^{\circ}+\cos 20^{\circ}+\cos 30^{\circ}=$
→
If the lines x + y = 6 and x + 2y = 4 be diameters of the circle whose diameter is 20, then the equation of the circle is
→
$\lim _{x \rightarrow \infty} x^3\left\{\sqrt{x^2+\sqrt{1+x^4}}-x \sqrt{2}\right\}=$
→
If $\tan \alpha=\frac{1}{7}$ and $\tan \beta=\frac{1}{3}$, then $\cos 2 \alpha=$
→
$\lim _{x \rightarrow 0}\left[\frac{\left(3^{\sin x}-1\right)^3}{\left(3^x-1\right) \cdot \tan x \cdot \log (1+x)}\right]=$
→
The value(s) of r for which the function
$f(x)=\left\{\begin{array}{cc}1-x , & x<1 \$1-x)(2-x) , & 1 \leq x \leq 2 \\3-x , & x>2\end{array}\right.$
fails to be continuous is (are)
→
The mean of 5 observations is 4.4 and variance is 8.24. If three of the five observations are 1,2 and 6 , then the values of other two observations are
→
If $f: R \rightarrow R$ is defined by
$f(x)=\left\{\begin{array}{ll}x-1, & \text { for } x \leq 1 \\2-x^2, & \text { for } 1 < x \leq 3 \\x-10, & \text { for } 3 < x< 5 \\2 x, & \text { for } x \geq 5\end{array}\right.$
then the set of points of discontinuity of $f$ is
→