Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 26

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

Find the interval for which the function given by the following expression is continuous:

$f (x) = \frac{3 x + 7}{x^{2} - 5 x + 6}$ .

Important Questions on Continuity and Differentiability

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 27

Find the interval for which the function given by the following expression is continuous:

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

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 28

Find the interval for which the function given by the following expression is continuous:

$f (x) = \frac{\sqrt{x^{2} + 1}}{1 + \sin^{2} x}$ .

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 29

Find the interval for which the function given by the following expression is continuous:

$f (x) = \tan (\frac{π x}{2})$

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 30

If

f (x) = x + \{- x\} + [x],

where

[.]

is the integral part &

\{.\}

is the fractional part function. Discuss the continuity in

[- 2, 2]

. Also find nature of each discontinuity.

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 31

If

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

and

g (x) = \tan x,

then discuss the continuity of

f o g (x)

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 32

If

f (x) = \{\begin{cases} 1 + x; & 0 \leq x \leq 2 \\ 3 - x; & 2 < x \leq 3 \end{cases}

. Determine the composite function

g (x) = f (f (x)) &

hence find the point of discontinuity of

g

, if any.

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 33

Find the point of discontinuity of

y = f (u)

, where

f (u) = \frac{3}{2 u^{2} + 5 u - 3}

and

u = \frac{1}{x + 2} .

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-1>Q 34

Show that the function

f (x) = \frac{x^{3}}{4} - \sin π x + 3

takes the value

\frac{7}{3}

within the interval

[- 2, 2]

.