Limits and Continuity Test 48

Result

Limits and Continuity Test 48

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Weekly Quiz Competition

Question 1
1 / -0

If $$\underset { x\rightarrow 0 }{ lim } \dfrac { { x }^{ 3 } }{ \sqrt { a+x } (bx-sinx) } =1,$$ a > 0, then a + b is equal to

A
36

B
37

C
38

D
40

Solution
Question 2
1 / -0

$$\displaystyle\lim_{x\rightarrow 0}\dfrac{(1-\cos 2x)\sin 5x}{x^2\sin 3x}=?$$

A
$$10/3$$

B
$$3/10$$

C
$$6/5$$

D
$$56$$

Solution
Question 3
1 / -0

$$\underset { x\rightarrow 0 }{ lim } \dfrac { 1-\cos { 2x } }{ \cos { 2x } -\cos { 8x } } $$ is equal to

A
$$-1/15$$

B
$$1/10$$

C
$$1/15$$

D
$$15$$

Solution
Question 4
1 / -0

The value of $$\underset { x\rightarrow 0 }{ lim } \frac { { 27 }^{ x }-{ 9 }^{ x }{ -3 }^{ x }+1 }{ \sqrt { 5 } -\sqrt { 4+cos\quad x } } $$

A
$$\sqrt { 5 } { \left( log3 \right) }^{ 2 }$$

B
$$8\sqrt { 5 } log3$$

C
$$16\sqrt { 5 } log3$$

D
$$8\sqrt { 5 } { \left( log3 \right) }^{ 2 }$$

Solution
Question 5
1 / -0

$$\lim _ { x \rightarrow - 1 } \dfrac { \cos 2 - \cos 2 x } { x ^ { 2 } - | x | }$$ is equal to :

A
$$0$$

B
$$\cos 2$$

C
$$2 \sin 2$$

D
None

Solution
Question 6
1 / -0

$$\lim _ { x \rightarrow 0 } \dfrac { \sin 4 x } { \tan 7 x } =$$

A
$$1$$

B
$$\dfrac { 4 } { 7 }$$

C
$$\dfrac { 7 } { 4 }$$

D
$$0$$

Solution
Question 7
1 / -0

$$\lim _{ x\rightarrow 0 }{ \cfrac { x.{ 10 }^{ x }-x }{ 1-cosx } = } $$

A
$$\log { 10 } $$

B
$$2\log { 10 } $$

C
$$3\log { 10 } $$

D
$$4\log { 10 } $$

Solution
Question 8
1 / -0

$$\lim _ { x \rightarrow 0 } \dfrac { \sin x ^ { 5 } } { \sin ^ { 4 } x } =$$

A
$$0$$

B
$$1$$

C
$$-1$$

D
$$\infty$$

Solution
Question 9
1 / -0

$$\lim _ { x \rightarrow 1 } \left( \log _ { 3 } 3 x \right) ^ { \log _ { x } 3 } =?$$

A
$$e ^ { - 1 }$$

B
$$e$$

C
$$-1$$

D
$$1$$

Solution
Question 10
1 / -0

Let $$f ( \beta ) = \lim _ { \alpha \rightarrow \beta } \dfrac { \sin ^ { 2 } \alpha - \sin ^ { 2 } \beta } { \alpha ^ { 2 } - \beta ^ { 2 } },$$ then $$f \left( \dfrac { \pi } { 4 } \right)$$ is greater than-

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

B
$$\lim _ { x \rightarrow \pi / 2 } \dfrac { \cot x - \cos x } { ( \pi - 2 x ) ^ { 3 } }$$

C
$$\lim _ { x \rightarrow \infty } ( \cos \sqrt { x + 1 } - \cos \sqrt { x } )$$

D
$$\lim _ { x \rightarrow a } \dfrac { \sqrt { a + 2 x } - \sqrt { 3 x } } { \sqrt { 3 a + x } - 2 \sqrt { x } }$$ where $$a > 0$$

Solution