Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 26

MEDIUM

JEE Main

IMPORTANT

Earn 100

If both $f (x)$ and $g (x)$ are differentiable functions at $x = x_{0}$ , then the function defined as $h (x) =$ maximum $\{f (x), g (x)\}$

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Important Questions on Continuity and Differentiability

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 27

If

f (x) = \{\begin{matrix} \frac{x \cdot l n (c o s x)}{l n (1 + x^{2})}, & x \neq 0 \\ 0, & x = 0 \end{matrix}

, then

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 28

Let

[x]

denotes the greatest integer less than or equal to

x

. If

f (x) = [x s i nπ x]

, then

f (x)

is:

MEDIUM

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 29

The function

f (x) = [|x|] - |[x]|

, where

[x]

denotes greatest integer function

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 30

The function

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

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 31

Consider the function

f (x) = |x^{3} + 1|

. Then,

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JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 32

f

is a continuous function in

[a, b], g

is a continuous function in

[b, c]

. A function

h (x)

is defined as

h (x) = \{\begin{matrix} f (x) for x \in [a, b) \\ g (x) for x \in (b, c] \end{matrix}

. If

f (b) = g (b)

, then:

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JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 33

Which of the following function(s) has/have the same range?

HARD

JEE Main

IMPORTANT

Skills in Mathematics Differential Calculus for JEE Main & Advanced>Chapter 6 - Continuity and Differentiability>Proficiency in 'Continuity and Differentiability' Exercise 1>Q 34

If

f (x) = s e c 2 x + c o s e c 2 x

, then

f (x)

is discontinuous at all point in: