Limits and Continuity Test 52

Result

Limits and Continuity Test 52

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Weekly Quiz Competition

Question 1
1 / -0

$$\underset { \theta \longrightarrow 0 }{ Lt } \dfrac { 3tan\theta -tan3\theta }{ { 2\theta }^{ 3 } } =$$

A
1/4

B
3/4

C
4

D
-4

Solution
Question 2
1 / -0

$$\underset { x\rightarrow 0 }{ lim } \dfrac { 1 }{ { e }^{ 2 } } tan\left( \dfrac { \pi }{ 4 } +x \right) ^{ 1/x }$$

A
0

B
1

C
-1

D
e

Solution
Question 3
1 / -0

$$lim_{x \to 0^-} \dfrac{x([x]+ \mid x \mid )sin[x]}{\mid x \mid}$$ is equal to

A
$$-sin1$$

B
0

C
1

D
$$sin1$$

Solution
Question 4
1 / -0

$$L\underset { x\rightarrow \infty }{ im } \left( \sin { \sqrt { x+1 } -\sin { \sqrt { x } } } \right) =$$

A
2

B
-2

C
0

D
1
Question 5
1 / -0

$$\displaystyle\underset{x\rightarrow \dfrac{\pi}{4}}{Lt}\dfrac{\sqrt{2}-\cos x-\sin x}{(4x-\pi)^2}=?$$

A
$$\dfrac{1}{16\sqrt{2}}$$

B
$$\dfrac{1}{32\sqrt{2}}$$

C
$$\dfrac{1}{16}$$

D
$$\dfrac{1}{8}$$

Solution
Question 6
1 / -0

$$ \lim _{x \rightarrow 0} \frac{1-\cos ^{3} x}{x \sin 2 x}= $$

A
1$$ / 2 $$

B
3$$ / 2 $$

C
3$$ / 4 $$

D
1$$ / 4 $$

Solution
Question 7
1 / -0

$$L\underset { x\rightarrow 0 }{ im } \frac { \sec { 4x-\sec { 2x } } }{ \sec { 3x-\sec { x } } }=$$

A
3/2

B
2/3

C
1/3

D
3/4

Solution
Question 8
1 / -0

the value of $$\underset { x\rightarrow 0 }{ lim } \frac { sin\alpha X-sin\beta X }{ { e }^{ \alpha X }-{ e }^{ \beta X } } $$ equals

A
0

B
1

C
-1

D
$$\alpha -\beta $$

Solution
Question 9
1 / -0

$$\mathop {\lim }\limits_{h \to 0} \frac{{\sin \left( {a + 3h} \right) - 3\sin \left( {a + 2h} \right) + 3\sin \left( {a + h} \right) - \sin a}}{{{h^3}}}$$ is equal to

A
$$\cos a$$

B
$$ - \cos a$$

C
$$\sin a$$

D
$$\sin a\cos a$$

Solution
Question 10
1 / -0

The value of $$\underset { x\rightarrow 0 }{ lim } \left( \left( sinx \right) ^{ 1/x }+\left( \dfrac { 1 }{ x } \right) ^{ sinx } \right) $$ equals

A
0

B
1

C
$$\infty $$

D
-1

Solution