Limits and Derivatives Test

Result

Limits and Derivatives Test - 54

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Weekly Quiz Competition

Question 1
1 / -0

$$\lim _{ x\rightarrow 0 }{ \frac { { 27 }^{ x }-{ 9 }^{ x }-{ 3 }^{ x }+1 }{ \sqrt { 2 } -\sqrt { 1+\cos { x } } } = } $$

A
$$0$$

B
$$8\sqrt { 2 } { (\log { 3 } ) }^{ 2 }$$

C
$$8{ (\log { 3 } ) }^{ 2 }$$

D
$$1$$

Solution
Question 2
1 / -0

$$\mathop {\lim }\limits_{x \to \infty } \left( {\dfrac{{{x^2}\sin \left( {\dfrac{1}{x}} \right) - x}}{{1 - \left| x \right|}}} \right) = $$

A
0

B
1

C
-1`

D
2

Solution
Question 3
1 / -0

$$\lim _{ x\rightarrow }{ 0 } \{ (sinx-x)/{ x }^{ 3 })\} $$ equals:

A
$$1/3$$

B
$$-1/3$$

C
$$1/6$$

D
$$-1/6$$

Solution
Question 4
1 / -0

$$ \lim _{x \rightarrow a}\left(2-\frac{a}{x}\right)^{\tan \left(\frac{\pi x}{2 a}\right)} $$

A
$$

e^{-\frac{a}{\pi}}

$$

B
$$

e^{-\frac{2 a}{\pi}}

$$

C
$$

e^{-\frac{2}{x}}

$$

D
1

Solution
Question 5
1 / -0

$$\lim _{ x\rightarrow 0 }{ \frac { \sin { [\cos { x } ] } }{ 1+[\cos { x } ] } } $$ is (where [] is G.I.F)

A
1

B
0

C
does not exist

D
2

Solution
Question 6
1 / -0

$$\mathop {\lim }\limits_{x \to \pi /2} \left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\sec x} \right]$$ is equal to

A
1

B
-1

C
0

D
None of these

Solution
Question 7
1 / -0

$$\underset { x\rightarrow a }{ lim } \left( \sin { \dfrac { x-a }{ 2 } \tan { \dfrac { \pi x }{ 2a } } } \right)$$

A
$$a/\pi$$

B
$$-a/\pi$$

C
$$\pi/a$$

D
$$-\pi/a$$

Solution
Question 8
1 / -0

The value of $$\mathop {{\text{Limit}}}\limits_{x \to 0} \frac{{\cos \left( {\sin x} \right) - \cos x}}{{{x^4}}}$$ is equal to

A
1/5

B
1/6

C
1/4

D
1/2

Solution
Question 9
1 / -0

$$\displaystyle \lim _{ x\rightarrow 0 }{ \left[ \dfrac { 100\tan { x } .\sin { x } }{ { x }^{ 2 } } \right] } $$ where $$[.]$$ represents greatest integer function is

A
$$99$$

B
$$100$$

C
$$0$$

D
$$98$$

Solution
Question 10
1 / -0

The value of $$\lim _ { x \rightarrow \dfrac { 1 } { 2 } } \dfrac { 2 \sin ^ { - 1 } x - \dfrac { \pi } { 2 } } { 1 - 2 x ^ { 2 } }$$ is equal to

A
$$-1$$

B
$$0$$

C
$$1$$

D
$$2$$

Solution