Limits and Derivatives Test

Result

Limits and Derivatives Test - 46

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$\underset{x \rightarrow 0}{lim} \cos \,ec^4 \,x \displaystyle \overset{x^2}{\underset{0}{\int}} \dfrac{In(1 + 4t)}{1 + t^2}dt$$ is

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution
Question 2
1 / -0

If $$g(x)=\frac { x }{ \left[ x \right] } for\quad x>2\quad then\quad \underset { x\rightarrow { 2 }^{ + } }{ Lim } \frac { g\left( x \right) -g\left( 2 \right) }{ x-2 } $$

A
-1

B
0

C
1/2

D
1

Solution
Question 3
1 / -0

$$\lim_{x\rightarrow 0}\frac{ln(sin 3x)}{ln(sin x)}$$ is equal to

A
0

B
1

C
2

D
Non existent

Solution
Question 4
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 5
1 / -0

$$\underset{x \rightarrow 2}{lim} \dfrac{\sqrt[3]{60 + x^2} - 4}{\sin (x - 2)}$$ equals

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

B
$$0$$

C
$$\dfrac{1}{12}$$

D
Does not exist

Solution
Question 6
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
Question 7
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 8
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 9
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 10
1 / -0

$$P= \lim_{x \rightarrow o^{+}} (1+ \tan^{2} \sqrt{x})^{1/2x}=$$____

A
$$P=1/4$$

B
$$P=1/2$$

C
$$P=2$$

D
$$P=1$$

Solution