MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 59

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The approximate value of $\tan 46 °$ is (given $1 ° = 0.0175$ radians)

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Important Questions on Applications of Derivatives

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 60

If

\log_{e} 3 = 1.0986

, then

\log_{e} (9.01)

approximately is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 61

The Rolle's theorem is applicable in the interval

- 1 \leq x \leq 1

for the function

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 62

Rolle's theorem is not applicable to the function

f (x) = | x |

for

- 2 \leq x \leq 2

because

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 63

Consider the function

f (x) = e^{- 2 x} \sin 2 x

over the interval

(0, \frac{π}{2})

. A real number

c \in (0, \frac{π}{2})

as guaranteed by Rolle's theorem such that

f^{'} (c) = 0

, is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 64

If the function

f (x) = x^{3} - 6 x^{2} + a x + b

satisfies Rolle's theorem in the interval

[1, 3]

and

f^{'} (\frac{2 \sqrt{3} + 1}{\sqrt{3}}) = 0

, then

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 65

The function

f (x) = x (x + 3) e^{- (\frac{1}{2})} x

satisfies all the conditions of Rolle's theorem in

[- 3, 0]

. The value of

c

is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 66

If

f (x) = x^{α} \log x

and

f (0) = 0

, then the value of

α

for which Rolle's theorem can be applied in

[0, 1]

is

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IMPORTANT

MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 2 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 4 - Applications of Derivatives>Critical Thinking>Q 67

The value of

c

in Lagrange's mean value theorem for the function

f (x) = \log_{e} x

in the interval

[1, 3]

is