Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 66

HARD

JEE Advanced

IMPORTANT

Earn 100

If $f (x) = [\log_{e} x] + \sqrt{\{\log_{e} x\}}, x > 1$ , where $[]$ and $\{\}$ denote the greatest integer function and the fractional part function respectively, 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 67

If

f (2 + x) = f (- x)

for all

x \in R

, then differentiability at

x = 4

implies differentiability at

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 68

The number of points of non-differentiability for

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

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 69

If

f (x) = x^{3} sgn x

, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 70

If

f (x) = \{\begin{cases} |1 - 4 x^{2}|, & 0 \leq x < 1 \\ [x^{2} - 2 x], & 1 \leq x < 2 \end{cases}

, where

[]

denotes the greatest integer function, then

f (x)

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 5 - Continuity and Differentiability>Target Exercises>Q 71

If

f (x) = \{\begin{array}{cl} x - 1, & x < 0 \\ x^{2} - 2 x, & x \geq 0 \end{array}

, then