Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 51

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JEE Advanced

IMPORTANT

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Let $f (x) = \frac{1}{[\sin x]}$ , where $[\cdot]$ denotes the greatest integer function, then

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Important Questions on Continuity and Differentiability

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 52

The points, where the function

f (x) = [x] + |1 - x|, 1 \leq x \leq 3

, (where

[\cdot]

denotes the greatest integer function) is not differentiable, are

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 53

Let

f (x) = [n + p \sin x]; x \in (0, π), n \in I, p

is prime number and

[x]

denotes the greatest integer less than or equal to

x

. Then, the number of points at which

f (x)

is not differentiable, is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 54

If

f (x) = - {(- 1)}^{[x^{3}]}

, where

[\cdot]

denotes the greatest integer function, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 55

If

f (x) = \cos^{- 1} (\frac{2 x}{1 + x^{2}})

, then

f (x)

is differentiable on

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 56

Let

f (x)

be a function, satisfying the condition

f (- x) = f (x)

, for all real

x

. If

f^{'} (0)

exists, then its value is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 57

Let

f : R \to R

be a function such that

f (\frac{x + y}{3}) = \frac{f (x) + f (y)}{3}, f (0) = 0

and

f^{'} (0) = 3

Then,

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 58

If

f

is differentiable function satisfying

f (0) = 0

and

g (x) = \frac{f (x)}{x}

, then the value that should be assigned to

g (0)

, so that

g

is continuous at

x = 0

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 59

If

f (x + y) = 2 f (x) \cdot f (y)

for all

x, y

, where

f^{'} (0) = 3

and

f (4) = 2

then

f^{'} (4)

is equal to