Limits and Continuity Test 50

Result

Limits and Continuity Test 50

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$\begin{matrix} lim \\ x\rightarrow 0 \end{matrix}$$ $$[\frac{x}{sinx}],$$ where [.] represents the greatest inter function , is

A
$$1$$

B
$$0$$

C
$$-1$$`

D
none of these

Solution
Question 2
1 / -0

$$\underset { x\rightarrow 0 }{ lim } \left( \dfrac { 1+tanx }{ 1+sinx } \right) ^{ cosecx }$$ is equal to

A
e

B
$$\dfrac { 1 }{ e } $$

C
1

D
None of these

Solution
Question 3
1 / -0

The value of $$\displaystyle \lim_{x\rightarrow 0}\left(\dfrac {1}{x^{2}}-\cot x\right)$$ equals

A
$$1$$

B
$$0$$

C
$$\infty$$

D
$$Does\ not\ exist$$

Solution
Question 4
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 5
1 / -0

$$\underset { x\rightarrow 0 }{ Lt\quad } \frac { sec\quad x-1 }{ { \left( sec\quad x+\quad 1 \right) }^{ 2 } } =$$

A
1/8

B
11/4

C
3.2

D
2
Question 6
1 / -0

Value of $$\underset { x\rightarrow 0 }{ lim } \dfrac { \sqrt [ 3 ]{ 1+\tan { x } } -\sqrt [ 3 ]{ 1-\tan { x } } }{ x } $$ is

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

B
$$-\dfrac { 2 }{ 3 } $$

C
$$\dfrac { 1 }{ 3 } $$

D
$$0$$
Question 7
1 / -0

If $$\begin{matrix} lim\quad \\ x\rightarrow 0 \end{matrix}\dfrac { x\left( 1+acosx \right) -bsinx }{ { x }^{ 3 } } =1$$ then value of a + b

A
-4

B
-6

C
1

D
None of these
Question 8
1 / -0

$$\underset { x\rightarrow 0 }{ Lt } (1+sin\quad x)^{ cot\quad x }=$$

A
e

B
$$e^{ 2 }$$

C
$$e^{ 3 }$$

D
$$e^{ 4 }$$

Solution
Question 9
1 / -0

Value of $$\underset { x\rightarrow \dfrac { \pi }{ 2 } }{ lim } \tan { x } .\ell nsin{ x }$$ is

A
0

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

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

D
None of these
Question 10
1 / -0

For $$a > 1$$ then $$\displaystyle\lim_{x\rightarrow \infty}\dfrac{a^x-a^{-x}}{a^x+a^{-x}}=?$$

A
$$1$$

B
$$1/2$$

C
$$1/3$$

D
$$1/15$$

Solution