If $$u=f(x^{2}), v=g(x^{3}),f(x)=sinx, g^{1}(x)=cosx$$ then find $$\frac{du}{dv}$$

$$\frac{2sin x^{2}}{3xcos x^{3}}$$

MCQ Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 14

$\displaystyle\lim _{ x\rightarrow 0 }{ \dfrac { x\tan { 2x } -2x\tan { x } }{ \left( 1-\cos { 2x } \right) ^{ 2 } } }$ equal to

0%
$\dfrac{1}{4}$
0%
$1$
0%
$\dfrac{1}{2}$
0%
$None of these$

$\displaystyle\lim_{x\rightarrow \dfrac{\pi}{4}}\dfrac{\cos x-\sin x}{\left(\dfrac{\pi}{4}-x\right)(\cos x+\sin x)}=?$

0%
$2$
0%
$1$
0%
$0$
0%
$3$

$\lim _{x \rightarrow 0}\left(\cos x+a^{3} \sin \left(b^{6} x\right)\right)^{\frac{1}{x}}=e^{512}$ then value of

$ab^2$ is equal to

0%
$-512$
0%
$512$
0%
$8$
0%
none of these

$if\left( x \right) =\left[ x-3 \right] +\left[ x-4 \right] \quad for\quad x\epsilon R\quad then\quad \underset { x\rightarrow 3 }{ lim } f\left( x \right) =$

0%
-2
0%
-1
0%
0
0%
2

The value of

$\int _{ 0 }^{ \left[ x \right] }{ \left( x-\left[ x \right] \right) dx\quad is\left( \left[ . \right] denotes\quad greatest\quad integer\quad function \right) }$

0%
$\left[ x \right]$
0%
$2\left[ x \right]$
0%
$\dfrac { \left[ x \right] }{ 2 }$
0%
$3\left[ x \right]$

$\underset { x\rightarrow 0 }{ lim } \dfrac { 1-\cos { 2x } }{ \cos { 2x } -\cos { 8x } }$ is equal to

0%
$-1/15$
0%
$1/10$
0%
$1/15$
0%
$15$

The value of

$\underset { x\rightarrow 0 }{ lim } \frac { { 27 }^{ x }-{ 9 }^{ x }-{ 3 }^{ x }+1 }{ \sqrt { 5 } -\sqrt { 4+cosx } }$ is

0%
$\sqrt { 5 } { \left( log3 \right) }^{ 2 }$
0%
$8\sqrt { 5 } log3$
0%
$16\sqrt { 5 } log3$
0%
$8\sqrt { 5 } { \left( log3 \right) }^{ 2 }$

$\lim _{ x\rightarrow 0 }{ \cfrac { x.{ 10 }^{ x }-x }{ 1-cosx } = }$

0%
$\log { 10 }$
0%
$2\log { 10 }$
0%
$3\log { 10 }$
0%
$4\log { 10 }$

$\displaystyle \lim _ { x \rightarrow 0 } \dfrac { | \cos ( \sin ( 3 x ) ) | - 1 } { x ^ { 2 } }$ equals

0%
$\dfrac { - 9 } { 2 }$
0%
$\dfrac { - 3 } { 2 }$
0%
$\dfrac { 3 } { 2 }$
0%
$\dfrac { 9 } { 2 }$

$\displaystyle \lim _ { x \rightarrow 0 } \left( \left[ \dfrac { - 5 \sin x } { x } \right] + \left[ \dfrac { 6 \sin x } { x } \right] \right)$ (where

$[ .]$ denotes greatest integer function) is equal to

0%
$0$
0%
$-12$
0%
$1$
0%
$2$

$\underset { x\rightarrow 0 }{ lim } \dfrac { { x }^{ 3 } }{ \sqrt { a+x } (bx-sinx) } =1,$ a > 0, then a + b is equal to

0%
36
0%
37
0%
38
0%
40

$\underset { x\rightarrow 0 }{ lim } \frac { sin({ 6x }^{ 2 }) }{ Incos({ 2x }^{ 2 }-x) } =$

0%
12
0%
-12
0%
6
0%
-6

$\underset { x\rightarrow -\infty }{ lim } \frac { ({ 3x }^{ 4 }+{ 2x }^{ 2 })sin(\frac { 1 }{ x } )+{ |x| }^{ 3 }+5 }{ { |x }|^{ 3 }+{ |x| }^{ 2 }+|x|+1 } =$

0%
2
0%
1
0%
-2
0%
-3

$\underset { x\rightarrow \frac { \pi }{ 2 } }{ lim } \frac { cotx-cosx }{ { (\pi -2x) }^{ 3 } }$ equals :

0%
$\frac { 1 }{ 8 }$
0%
$\frac { 1 }{ 4 }$
0%
$\frac { 1 }{ 24 }$
0%
$\frac { 1 }{ 16 }$

Let

$f\left( x \right)=asin\left| x \right| +{ be }^{ \left| x \right| }$ is differentiable when

0%
$a=-b$
0%
$a=b$
0%
$a-0$
0%
$b=0$

The value of

$\displaystyle \lim_{x\rightarrow 0}\left(\dfrac {1}{x^{2}}-\cot x\right)$ equals

0%
$1$
0%
$0$
0%
$\infty$
0%
$Does\ not\ exist$

$\underset { \theta \longrightarrow 0 }{ Lt } \dfrac { 3tan\theta -tan3\theta }{ { 2\theta }^{ 3 } } =$

0%
1/4`
0%
3/4
0%
4
0%
-4

$\underset { x\rightarrow 0 }{ Lt\quad } \frac { sec\quad x-1 }{ { \left( sec\quad x+\quad 1 \right) }^{ 2 } } =$

0%
1/8
0%
11/4
0%
3.2
0%
2

$u=f(x^{2}), v=g(x^{3}),f(x)=sinx, g^{1}(x)=cosx$ then find

$\frac{du}{dv}$

0%
$1$
0%
$\frac{2}{3}$
0%
$\frac{2sin x^{2}}{3xcos x^{3}}$
0%
$\frac{2x^{2}}{3x^{3}}$

$\begin{matrix} lim\quad \\ x\rightarrow 0 \end{matrix}\dfrac { x\left( 1+acosx \right) -bsinx }{ { x }^{ 3 } } =1$ then value of a + b

0%
-4
0%
-6
0%
1
0%
None of these

Value of

$\underset { x\rightarrow 0 }{ lim } \dfrac { \sqrt [ 3 ]{ 1+\tan { x } } -\sqrt [ 3 ]{ 1-\tan { x } } }{ x }$ is

0%
$\dfrac { 1 }{ 2 }$
0%
$-\dfrac { 2 }{ 3 }$
0%
$\dfrac { 1 }{ 3 }$
0%
$0$

$\lim _{ x\rightarrow 0 }{ \frac { \sqrt [ 3 ]{ 1+\sin { x } } -\sqrt [ 3 ]{ 1-\sin { x } } }{ x } } =$

0%
$0$
0%
$1$
0%
$\frac { 2 }{ 3 }$
0%
$\frac { 3 }{ 2 }$

Value of

$\underset { x\rightarrow \dfrac { \pi }{ 2 } }{ lim } \tan { x } .\ell nsin{ x }$ is

0%
0
0%
$\dfrac { 1 }{ 2 }$
0%
$\dfrac { 3 }{ 4 }$
0%
None of these

$cosy=xcos(a+y)and\quad \cfrac { dy }{ dx } =\cfrac { k }{ 1+{ x }^{ 2 }-2xcosa }$ then find value of k?

0%
sin a
0%
cos a
0%
1
0%
-sin a

$\underset { x\rightarrow 0 }{ lim } \left( \dfrac { 1+tanx }{ 1+sinx } \right) ^{ cosecx }$ is equal to

0%
e
0%
$\dfrac { 1 }{ e }$
0%
1
0%
None of these

The value of

$\displaystyle \lim _{ x\rightarrow \infty } (|x^{2}|+x)\log{(x\cot^{-1}{x})}$ is :

0%
$\dfrac{1}{3}$
0%
$-\dfrac{1}{3}$
0%
$\dfrac{2}{3}$
0%
$-\dfrac{2}{3}$

$\displaystyle \lim _{ x\rightarrow \dfrac { \pi }{ 2 } }{ \dfrac { \sin { x } }{ \cos ^{ -1 }{ \left[ \dfrac { 1 }{ 4 } \left( 3\sin { x } -\sin { 3x } \right) \right] } } }$ , where [.] denotes greatest integer function is :

0%
$\dfrac{2}{\pi}$
0%
$1$
0%
$\dfrac{4}{\pi}$
0%
$does\ not\ exist$

$\lim _ { x \rightarrow \frac { \pi } { 2 } } \left( \frac { 1 + \cos x } { 1 - \cos x } \right) ^ { \sec x } =$

0%
e
0%
$e^2$
0%
$e^3$
0%
$e/4$

$Im _{ }{ \left( \dfrac { 1 }{ 1-\cos { \theta } +i\sin { \theta } } \right) }$ is equal to

0%
$\dfrac{1}{2}\tan\dfrac{\theta}{2}$
0%
$\dfrac{1}{2}\cot\dfrac{\theta}{2}$
0%
$-\dfrac{1}{2}\tan\dfrac{\theta}{2}$ `
0%
$-\dfrac{1}{2}\cot\dfrac{\theta}{2}$

$L\underset { x\rightarrow 0 }{ im } \frac { \sec { 4x-\sec { 2x } } }{ \sec { 3x-\sec { x } } }=$

0%
3/2
0%
2/3
0%
1/3
0%
3/4

CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 14 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

CBSE Questions for Class 11 Engineering Maths Limits And Derivatives Quiz 14 - MCQExams.com

0:0:4

Practice Class 11 Engineering Maths Quiz Questions and Answers

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