Limits and Continuity Test 40

Result

Limits and Continuity Test 40

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$lim_{x\to 0} \dfrac{sin(\pi cos^2 x)}{x^2}$$ equals

A
$$-\pi$$

B
$$\pi$$

C
$$\dfrac{\pi}{2}$$

D
$$2 \pi$$

Solution
Question 2
1 / -0

The value of $$\lim _{ x\rightarrow 0 }{ \dfrac { 1-\cos { ^{ 3 }x } }{ x\sin { x\cos { x } } } }$$ is

A
$$\dfrac{2}{5}$$

B
$$\dfrac{3}{5}$$

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

D
$$\dfrac{3}{4}$$

Solution
Question 3
1 / -0

The value of $$\displaystyle\lim _ { x \rightarrow \infty } a ^ { x } \sin \left( \frac { b } { a ^ { x } } \right)$$ where $$a > 1$$ is

A
$$b \log a$$

B
$$a \log b$$

C
$$b$$

D
$$a$$

Solution
Question 4
1 / -0

The value of $$\displaystyle \lim _{ x\rightarrow 3 }{ \dfrac { \left( { x }^{ 3 }+27 \right) \log _{ e }{ \left( x-2 \right) } }{ { x }^{ 2 }-9 } } $$ is

A
$$9$$

B
$$18$$

C
$$27$$

D
$$\dfrac {1}{3}$$

Solution
Question 5
1 / -0

$$\underset { x\rightarrow 1 }{ lim } \frac { xtan(x-[x]) }{ x-1 } $$ is:

A
1

B
0

C
-1

D
does not exist

Solution
Question 6
1 / -0

The value of $$\displaystyle \lim_{x \rightarrow 0} \left(\dfrac{\sin x}{x}\right)^{1/x^{2}}$$ is

A
$$e^{-1/6}$$

B
$$e^{1/6}$$

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

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

Solution
Question 7
1 / -0

$$\lim_{x\rightarrow 0 }(\frac{p^{\frac{1}{x}}+q^{\frac{1}{x}}+r^{\frac{1}{x}}+s^{\frac{1}{x}}}{4})3x $$ where p,q,r,s$$> 0 $$ is equal to

A
$$pqrs$$

B
$$(pqrs)^{3}$$

C
$$(pqrs)\frac{3}{2}$$

D
$$(pqrs)\frac{3}{4}$$
Question 8
1 / -0

The value of $$lim_{\theta \to \dfrac{\pi}{2}} (sec \theta - tan \theta)$$ equals

A
$$0$$

B
$$1$$

C
$$2$$

D
$$\infty$$

Solution
Question 9
1 / -0

$$\lim- {x\to 0}$$ $$\dfrac{1- cos(1 - cos4x)}{x^4}$$ is equal to :

A
4

B
16

C
32

D
None of these

Solution
Question 10
1 / -0

If $$\displaystyle \lim _{ x\rightarrow 0 }{ \dfrac { \left( \sin { nx } \right) \left[ (a-n)nx-tanx \right] }{ { x }^{ 2 } } } =0$$, then the value of $$a$$

A
$$\dfrac { 1 }{ n }$$

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

C
$$n+\dfrac{1}{n}$$

D
$$None\ of\ these$$

Solution