_ x ( 1 - 4 x - 1 )^ 3x - 1 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to \infty } {\left( {1 - \frac{4}{{x - 1}}} \right)^{3x - 1}} = $

A
${e^{12}}$
✓
${e^{ - 12}}$
C
${e^4}$
D
${e^3}$

✓

Answer

Correct option: B.

${e^{ - 12}}$

b
(b) $\mathop {\lim }\limits_{x \to \infty } {\left( {1 - \frac{4}{{x - 1}}} \right)^{3x - 1}} = \mathop {\lim }\limits_{x \to \infty } {\left[ {{{\left( {1 + \frac{{( - 4)}}{{x - 1}}} \right)}^{\left( {\frac{{x - 1}}{{ - 4}}} \right)}}} \right]^{\left( {\frac{{ - 4}}{{x - 1}}} \right)(3x - 1)}}$

$ = {e^{\mathop {\lim }\limits_{x \to \infty } \left[ {\frac{{ - 4\left( {3 - \frac{1}{x}} \right)}}{{\left( {1 - \frac{1}{x}} \right)}}} \right]}} = {e^{ - 12}}$.

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 12. limits→12. limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If two sets $A$ and $B$ are having $99$ elements in common, then the number of elements common to each of the sets $A \times B$ and $B \times A$ are

The equation of the circle of radius $5$ and touching the coordinate axes in third quadrant is

The number of elements in the set $S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^2 \theta+2=0\right\}$ is $...........$.

For the three events $A, B$ and $C, P$ (exactly one of the events $A$ or $B$ occurs) = $P$ (exactly one of the events $B$ or $C$ occurs)= $P$ (exactly one of the events $C$ or $A$ occurs)= $p$ and $P$ (all the three events occur simultaneously) $ = {p^2},$ where $0 < p < 1/2$. Then the probability of at least one of the three events $A, B$ and $C$ occurring is

If, $(\text{a}+1)\text{x}^2+2(\text{a}+1)\text{x}+(\text{a}-2)=0$ then, for what parameter of ‘a’ the given equation have imaginary roots?

If the constant term in the expansion of $\left(1+2 x-3 x^3\right)\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9$ is $p$, then $108$ p is equal to....................

The value of ${(8)^{1/3}}$ is

There are $(n + 1)$ white and $(n + 1)$ black balls each set numbered $1$ to $n + 1$. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different colours is

The equation of the circle with origin as centre passing the vertices of an equilateral triangle whose median is of length $3a$ is

The centre of the circle passing through $(0, 0)$ and $(1, 0)$ and touching the circle ${x^2} + {y^2} = 9$ is