# Limits and Derivatives

This set of MCQs is based on the concepts and learning about limits and derivatives, which are extremely crucial concepts in mathematics whose application is not only limited to mathematics but are also present in other subjects like physics.

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What is the value of $$\lim\limits_{y \rightarrow \pi/2}\frac{sin⁡ x}{x}$$?

$$\frac{2}{\pi}$$ $$\frac{\pi}{2}$$ 1 0

What is the value of $$\lim\limits_{y \rightarrow 0}\frac{sin⁡3y}{3y}$$?

0 1 3 $$\frac{1}{3}$$

What is the value of $$\lim\limits_{x \rightarrow 0}\frac{x^2sec x}{sin⁡ x}$$?

3 2 1 0

What is the value of $$\lim\limits_{x \rightarrow 0}\frac{x \,tanx}{cot\, x}$$?

0 1 2 $$\frac{1}{2}$$

What is the value of $$\lim\limits_{x \rightarrow \infty}\frac{x sin⁡\frac{2}{x}}{2}$$?

1 2 $$\frac{1}{2}$$ Limit does not exist

The derivative of x2 cos x is,

2x sin x – x2 sin x

2x cos x – x2 sin x

2x sin x – x2 cos x

cosx – x2 sin x cos x

limx→0 | sin x|/x is equal to,

1

–1

0

does not exist

If f(x) = x sin x, then f′(π/2) is equal to,

0

1

–1

1/2

limx→0 (cosec x – cot x)/x is,

-1/2

1

1/2

1

If f(x) = x100 + x99 + … + x + 1, then f′(1) is equal to,

5050

5049

5051

50051

Limx→0 log(1 – x) is equals to,

0

1

1/2

None of these

The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²), is

0

1

2

-2

Limx→0 {(ax – bx)/ x} is equal to,

log a

log b

log (a/b)

log (a×b)

Limx→0 {(ax – bx)/ x} is equal to,

log a

log b

log (a/b)

log (a×b)

The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is,

x × tan x × sec x

x × tan x × sec x + x × sec x

tan x × sec x + sec x

x × tan x × sec x + sec x

The expansion of log(1 – x) is,

x – x²/2 + x³/3 – ……..

x + x²/2 + x³/3 + ……..

-x + x²/2 – x³/3 + ……..

-x – x²/2 – x³/3 – ……..

The expansion of log(1 – x) is,

x – x²/2 + x³/3 – ……..

x + x²/2 + x³/3 + ……..

-x + x²/2 – x³/3 + ……..

-x – x²/2 – x³/3 – ……..

Quiz/Test Summary
Title: Limits and Derivatives
Questions: 17
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