Limits and Derivatives Test

Result

Limits and Derivatives Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

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

A
$$\dfrac { 1 }{ 2 } $$

B
$$-\dfrac { 2 }{ 3 } $$

C
$$\dfrac { 1 }{ 3 } $$

D
$$0$$
Question 2
1 / -0

$$\underset { x\rightarrow 0 }{ Lt } (1+sin\quad x)^{ cot\quad x }=$$

A
e

B
$$e^{ 2 }$$

C
$$e^{ 3 }$$

D
$$e^{ 4 }$$

Solution
Question 3
1 / -0

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

A
$$0$$

B
$$1$$

C
$$\dfrac { 1 }{ e } $$

D
None of these

Solution
Question 4
1 / -0

$$\underset { x\rightarrow 0 }{ lim } \dfrac { 1 }{ { e }^{ 2 } } tan\left( \dfrac { \pi }{ 4 } +x \right) ^{ 1/x }$$

A
0

B
1

C
-1

D
e

Solution
Question 5
1 / -0

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

A
sin a

B
cos a

C
1

D
-sin a

Solution
Question 6
1 / -0

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

A
e

B
$$\dfrac { 1 }{ e } $$

C
1

D
None of these

Solution
Question 7
1 / -0

$$\lim_{x\rightarrow 1}\dfrac {1+\sin \pi\left(\dfrac {3x}{1+x^{2}}\right)}{1+\cos \pi x}$$ is equal to

A
$$0$$

B
$$1$$

C
$$2$$

D
$$4$$
Question 8
1 / -0

$$lim_{x \to 0^-} \dfrac{x([x]+ \mid x \mid )sin[x]}{\mid x \mid}$$ is equal to

A
$$-sin1$$

B
0

C
1

D
$$sin1$$

Solution
Question 9
1 / -0

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

A
e

B
$$e^2$$

C
$$e^3$$

D
$$e/4$$
Question 10
1 / -0

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

A
$$\dfrac{1}{3}$$

B
$$-\dfrac{1}{3}$$

C
$$\dfrac{2}{3}$$

D
$$-\dfrac{2}{3}$$

Solution