Solve the following Question.(1 Marks)

Question 11 Mark

If $f(2)=4, f^{\prime}(2)=1$, then find $\lim _{x \rightarrow 2}\left[\frac{x f(2)-2 f(x)}{x-2}\right]$

Answer

$ \lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$
$=\lim _{x \rightarrow 2} \frac{f(2)-2 f^{\prime}(x)}{1} \quad \ldots[\text { By L'Hospital Rule] }$
$=f(2)-2 f^{\prime}(2)$
$=4-2(1)=2 $
[By L' Hospital Rule]

View full question & answer→

Question 21 Mark

Differentiate the following w.r.t. x :
$y = e^x \log x$

View full question & answer→

Question 31 Mark

Differentiate the following w.r.t. x :
$y=\left(x^2+2\right)^2 \sin x$

View full question & answer→

Question 41 Mark

Differentiate the following w.r.t. x :
$y = x^3 \log\ x$

View full question & answer→

Question 51 Mark

Differentiate the following w.r.t. x :
$y = x^5\ tan\ x$

View full question & answer→

Question 61 Mark

Differentiate the following w.r.t. x :

$y=\sqrt{ } x+\tan x-x^3$

Answer

$y=\sqrt{x}+\tan x-x^3$
Differentiating w.r.t. $x$, we get
$\begin{aligned}
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(\sqrt{x}+\tan x-x^3\right) \\
\frac{ d y}{ d x} & =\frac{ d }{ d x}(\sqrt{x})+\frac{ d }{ d x}(\tan x)-\frac{ d }{ d x}\left(x^3\right) \\
& =\frac{1}{2 \sqrt{x}}+\sec ^2 x-3 x^2
\end{aligned}$

View full question & answer→

Question 71 Mark

Differentiate the following w.r.t. x :

$y =x^{\frac{4}{3}}+e^x-\sin x$

Answer

$
y=x^{\frac{4}{3}}+ e ^x-\sin x
$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(x^{\frac{4}{3}}+ e ^x-\sin x\right) \\
\frac{ d y}{ d x} & =\frac{ d }{ d x}\left(x^{\frac{4}{3}}\right)+\frac{ d }{ d x}\left( e ^x\right)-\frac{ d }{ d x}(\sin x) \\
& =\frac{4}{3} x^{\frac{4}{3}-1}+ e ^x-\cos x \\
& =\frac{4}{3} x^{\frac{1}{3}}+ e ^x-\cos x
\end{aligned}
$

View full question & answer→

Maths Solve the following Question.(1 Marks)

Take a timed test