Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 22

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AP EAPCET

IMPORTANT

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The number of points of discontinuity of the function $f (x) = x - [x]$ in the interval $(0, 7)$ are, where $[\cdot]$ is the greatest integer function.

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Important Questions on Continuity and Differentiability

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AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 23

If the function

f (x) = \{\begin{cases} x^{2}, if x \leq 4 \\ a x, if x > 4 \end{cases}

is continuous at

x = 4,

then

a =

EASY

AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 24

The number of points at which the function

f (x) = \frac{1}{\log |x|}

discontinuous is

HARD

AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 25

If the function,

f (x) = \{\begin{matrix} x + a^{2} \sqrt{2} \sin x, & 0 \leq x \leq \frac{π}{4} \\ x \cot x + b, & \frac{π}{4} \leq x \leq \frac{π}{2} \\ b \sin 2 x - a \cos 2 x, & \frac{π}{2} \leq x \leq π \end{matrix}

is continuous in the interval

[0, π]

then the value of

(a, b)

are

HARD

AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 26

Let $f (x) = \{\begin{cases} (x - 1) \sin (\frac{1}{x - 1}), & if x \neq 1 \\ 0 & , if x = 1 \end{cases}$ . Then which one of the following is true?

HARD

AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 27

The point of discontinuity of

f (x) = \tan (\frac{π x}{x + 1})

other than

x = - 1

are

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AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 28

Let

f (x) = \frac{1 - \tan x}{4 x - π}, x \neq \frac{π}{4}, x \in (0, \frac{π}{2})

. If

f (x)

is continuous in

(0, \frac{π}{2})

, then

f (\frac{π}{4}) =

EASY

AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 29

The number of discontinuous functions

y (x)

on

[- 2, 2]

satisfying

x^{2} + y^{2} = 4

is

HARD

AP EAPCET

IMPORTANT

Comprehensive Guide to AP EAPCET Mathematics>Chapter 9 - Continuity and Differentiability>Exercise 2>Q 30

Let

f (x) = \{\begin{array}{cl} \sin x, & for x \geq 0 \\ 1 - \cos x, & for x \leq 0 \end{array}

and

g (x) = e^{x}

. Then the value of

(g o f)^{'} (0)

is