Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 26

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Let $f : R \to R$ is a function satisfying $f (10 - x) = f (x)$ and $f (2 - x) = f (2 + x), \forall x \in R$ . If $f (0) = 101$ , then the minimum possible number of values of $x$ satisfying $f (x) = 101$ for $x \in [0, 30]$ is

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Important Questions on Continuity and Differentiability

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 27

Find the natural number

' a'

for which

\sum_{k = 1}^{n} f (a + k) = 2048 (2^{n} - 1)

, where the function

' f'

satisfies the relation

f (x + y) = f (x) \cdot f (y)

for all natural numbers

x & y

and further

f (1) = 2

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 28

Which of the following function(s) defined below has/have single point continuity?

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 29

The function

f (x) = \{\begin{matrix} | x - 3 |, & x \geq 1 \\ (\frac{x^{2}}{4}) - (\frac{3 x}{2}) + (\frac{13}{4}), & x < 1 \end{matrix}

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 30

If

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

then on the interval

[0, π]

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 31

Let

f (x)

and

g (x)

be defined by

f (x) = [x]

and

g (x) = \{\begin{array}{lc} 0, & x \in I \\ x^{2}, & x \in R - I \end{array} (where [.]

denotes the greatest integer function), then

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 32

Let

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

, where

[.]

denotes the greatest integer function. Then

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 33

The points at which the function,

f (x) = |x - 0.5| + |x - 1| + \tan x

does not have a derivative in the interval

(0, 2)

are

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Alpha Question Bank for Engineering: Mathematics>Chapter 26 - Continuity and Differentiability>Exercise-2>Q 34

f (x) = {(\sin^{- 1} x)}^{2} \cdot \cos (\frac{1}{x})

if

x \neq 0, f (0) = 0, f (x)

is