Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 26

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JEE Advanced

IMPORTANT

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The function $f (x) = [x] \cos (\frac{2 x - 1}{2}) π$ , where $[]$ denotes the greatest integer function, is discontinuous at

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Important Questions on Continuity and Differentiability

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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 27

Let a function

f : R \to R

satisfy the equation

f (x + y) = f (x) + f (y)

for all

x, y

. If the function

f (x)

is continuous at

x = 0

, then

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 28

Let

f

and

g

be differentiable functions satisfying

g^{'} (a) = 2, g (a) = b

and

f o g = I

(identity function). Then,

f^{'} (b)

is equal to

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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 29

If

f (x) = \{\begin{array}{cl} \frac{1}{e^{\frac{1}{x}} + 1}, & x \neq 0 \\ 0, & x = 0 \end{array}

, then

f (x)

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 30

The function

f (x) = \{\begin{array}{cl} \frac{x (e^{\frac{1}{x}} - e^{- \frac{1}{x}})}{e^{\frac{1}{x}} + e^{- \frac{1}{x}}}, & x \neq 0 \\ 0, & x = 0 \end{array}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 31

If

f (x) = \sum_{n = 0}^{\infty} \frac{x^{n}}{n!} {(\log_{e} a)}^{n}

, then at

x = 0, f (x)

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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 32

If

f (x) = x + \frac{x}{1 + x} + \frac{x}{{(1 + x)}^{2}} + \dots,

then at

x = 0, f (x)

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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 33

The function $f (x) \{\begin{array}{l} 1 - 2 x + 3 x^{2} - 4 x^{3} + \dots, \\ 1, \end{array} \begin{matrix} x \neq - 1 \\ x = - 1 \end{matrix}$ 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 34

If

f (x) = [\tan x]; x \in (0, \frac{π}{3})

, then

f^{'} (\frac{π}{4})

is equal to, where

[\cdot]

is the greatest integer function.