Q. $\lim\limits _{x \rightarrow 0}\left(1-\frac{1}{2^{x}}\right)\left(\frac{1}{\sqrt{\tan x+4}-2}\right)=$

KCETKCET 2022 Report Error

A

$\log 16$

B

does not exist

C

$3 \log 2$

D

$6 \log 2$

Solution:

$G . E=\lim\limits _{x \rightarrow 0}\left(\frac{2^{x}-1}{2^{x}}\right)\left(\frac{\sqrt{\tan x+4}+2}{\tan x+4-4}\right)$
$=\lim\limits _{x \rightarrow 0}\left(\frac{2^{x}-1}{x}\right) \frac{x}{\tan x}\left(\frac{\sqrt{\tan x+4}+2}{2^{x}}\right)$
$=\log 2.1 .4=4 \log 2=\log 16$

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Q. limx→0(1−12x)(1√tanx+4−2)=\lim\limits _{x \rightarrow 0}\left(1-\frac{1}{2^{x}}\right)\left(\frac{1}{\sqrt{\tan x+4}-2}\right)=

log16\log 16

does not exist

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Latest Updates

Q. $\lim\limits _{x \rightarrow 0}\left(1-\frac{1}{2^{x}}\right)\left(\frac{1}{\sqrt{\tan x+4}-2}\right)=$

$\log 16$

$3 \log 2$

$6 \log 2$

1. It is observed that $23 x+17 y=1$ for some integers $x$ and $y$ . Then $(x, y)=$

2. The sum of all the positive divisors of $180$ excluding $1$ and itself is

3. If $x+y+z=\pi$ then the value of $\begin{vmatrix}\sin (x+y+z) & \sin B & \cos z \\ -\sin B & 0 & \tan A \\ \cos (x+y) & -\tan A & 0\end{vmatrix}$ is

4. If the value of a third order determinant is $11$ , then the value of the determinant formed by the cofactors will be

5. If $A=\begin{bmatrix}1 & -1 & 2 \\ 2 & 3 & 1 \\ 1 & -2 & 3\end{bmatrix}$ then $\text{adj}\left(A^{-1}\right)=$

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

3. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

5. The value of $\int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx$ is