Limits and Continuity Test 51

Result

Limits and Continuity Test 51

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$\lim_{h\rightarrow 0}\left\{\dfrac {1}{h.(8+h)^{1/3}-\dfrac {1}{2h}}\right\}$$ equals

A
$$0$$

B
$$\dfrac {-4}{3}$$

C
$$\dfrac {-16}{3}$$

D
$$\dfrac {-1}{48}$$

Solution
Question 2
1 / -0

$$\underset { h\rightarrow 0 }{ lim } \quad \frac { (2+h)cos(2+h)-2cos2 }{ h } =$$

A
cos2-2sin2

B
cos2+2sin2

C
sin2-2cos2

D
sin2+2cos2

Solution
Question 3
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 4
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 5
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
Question 6
1 / -0

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

A
$$\dfrac{2}{\pi}$$

B
$$1$$

C
$$\dfrac{4}{\pi}$$

D
$$does\ not\ exist$$

Solution
Question 7
1 / -0

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

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

B
$$\dfrac{1}{2}\cot\dfrac{\theta}{2}$$

C
$$-\dfrac{1}{2}\tan\dfrac{\theta}{2}$$`

D
$$-\dfrac{1}{2}\cot\dfrac{\theta}{2}$$

Solution
Question 8
1 / -0

The value of $$\lim_{x\rightarrow 0}\left(\dfrac {e^{x}+e^{-x}-2}{x^{2}}\right)^{1/x^{2}}$$ equals

A
$$e^{1/2}$$

B
$$e^{1/4}$$

C
$$e^{1/3}$$

D
$$e^{1/12}$$

Solution
Question 9
1 / -0

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

A
0

B
1

C
3$$/ 2$$

D
2$$/ 3$$

Solution
Question 10
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