Limits and Continuity Test 44

Result

Limits and Continuity Test 44

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Weekly Quiz Competition

Question 1
1 / -0

$$\lim_{x\rightarrow 0}\dfrac{2\left(\sqrt{3}\sin\left(\dfrac{\pi}{6}+x\right)-\cos\left(\dfrac{\pi}{6}+x\right)\right)}{x\sqrt{3}\left(\sqrt{3}\cos x-\sin x\right)}$$

A
$$-1/3$$

B
$$2/3$$

C
$$4/3$$

D
$$-4/3$$

Solution
Question 2
1 / -0

$$\lim_{x\rightarrow \pi/4}\dfrac{2\sqrt{2}-\left(\cos x+\sin x\right)^{2}}{1-\sin 2x}$$ is equal to

A
1

B
$$2\sqrt{2}$$

C
$$\dfrac{4\sqrt{2}}{3}$$

D
$$does\ not\ exist$$

Solution
Question 3
1 / -0

the value of $$\underset { x\rightarrow \infty }{ lim } \frac { { x }^{ 5 } }{ { 5 }^{ x } } $$ is-

A
0

B
1

C
$${ e }^{ 5 }$$

D
$${ e }^{ -5 }$$

Solution
Question 4
1 / -0

$$\lim _ { x \rightarrow 5 } \frac { \sin ^ { 2 } ( x - 5 ) \tan ( x - 5 ) } { \left( x ^ { 2 } - 25 \right) ( x - 5 ) } =$$

A
1$$/ 10$$

B
$$1$$

C
$$0$$

D
$$-6$$

Solution
Question 5
1 / -0

$$\underset { x\rightarrow \pi /4 }{ Lim } \dfrac { 2\sqrt { 2 } \left( cosx+sinx \right) ^{ 3 } }{ 1-sin2x } =2$$ is equal to

A
$$\dfrac{3\sqrt{2}}{2}$$

B
$$2\sqrt{2}$$

C
$$\dfrac{4\sqrt{2}}{3}$$

D
$does \not \exist$$

Solution
Question 6
1 / -0

The value f $$\lim_{x\rightarrow \pi/4}\dfrac{\sqrt{1-\sqrt{\sin 2x}}}{\pi-4x}=$$

A
$$-\dfrac{1}{4}$$

B
$$\dfrac{1}{4}$$

C
$$\dfrac{1}{2}$$

D
$$None\ of\ these$$

Solution
Question 7
1 / -0

If $$\displaystyle \lim_{x\rightarrow 0}\dfrac {ae^{-x}-b\cos x-\dfrac {1}{2}cx}{x\cos x}=2$$ then the value of $$a+b+c$$ is-

A
$$4$$

B
$$-4$$

C
$$2$$

D
$$-2$$

Solution
Question 8
1 / -0

The value of $$\displaystyle \lim _{ x\rightarrow \frac { x }{ 4 } }{ \dfrac { 4\sqrt { 2 } -{ \left( \cos { x } +\sin { x } \right) }^{ 5 } }{ 1-\sin { 2x } } } $$ is

A
$$0$$

B
$$\sqrt {2}$$

C
$$5\sqrt {2}$$

D
$$3$$

Solution
Question 9
1 / -0

If $$\underset { x\rightarrow 0 }{ Lim } \dfrac { \left( 1+{ a }^{ 3 } \right) +8{ e }^{ 1/x } }{ 1+\left( 1-{ b }^{ 3 } \right) +{ e }^{ 1/x } } =2$$ then

A
$$a=1,b=2$$

B
$$a=1,b={-3}^{1/3}$$

C
$$a=2,b={3}^{1/3}$$

D
none of these

Solution
Question 10
1 / -0

$$\underset{x \rightarrow n/2}{lim} \dfrac{\cot x - \cos x}{(\pi - 2x)^3}$$ equals

A
$$\dfrac{1}{24}$$

B
$$\dfrac{1}{16}$$

C
$$\dfrac{1}{8}$$

D
$$\dfrac{1}{4}$$

Solution