Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.3>Q 29

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Earn 100

Use differentiation to approximate ${(26)}^{\frac{1}{3}}$ .

Important Questions on Application of Derivatives

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.3>Q 30

If the radius of a sphere is measured as

9 cm

with an error of

0.03 cm

, then find the approximate error in calculating its volume.

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.4>Q 31

On the interval

[0, 1]

, the function

x^{25} {(1 - x)}^{75}

takes its maximum value at the point

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.4>Q 32

Let $f (x) = \{\begin{cases} |x|, for 0 < |x| \leq 2 \\ 1, for x = 0 \end{cases}$ , then at $x = 0$ , $f$ has

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.4>Q 33

The two positive numbers

x

and

y

such that

x + y = 60

and

x y^{3}

is maximum, is given by

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.4>Q 34

Two sides of a triangle are given. The angle between them such that the area is maximum, is given by

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.4>Q 35

The rate of working of an engine is given by

R = 15 v + \frac{6000}{v}

, where

0 < v < 30

and

v

is the speed of engine. The value of

v

for which

R

is least, is given by

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.4>Q 36

Which fraction exceeds its

p^{th}

power by the greatest number possible?

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Gamma Question Bank for Engineering Mathematics>Chapter 25 - Application of Derivatives>EXERCISE 6.4>Q 37

Maximum volume of the cylinder which can be inscribed in a sphere of radius

5 \sqrt{3} cm

, is given by