Let f:[1/2,1] R be a positive,non constant function and differentiable function such that f’(x)(first deriative)<2f(x) and f(1/2)=1Then the value of a=1/2,b=1 lies in the intervalA (2e-1,2e)B (e-1,2e-1)C (e-1/2,e-1)D (0,e-1/2)Multiple correctPlease answer quickly

Let f:[1/2,1] R be a positive,non constant function and differentiabl

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Integral Calculus> Let f:[1/2,1] R be a positive,non constan...

Let f:[1/2,1] R be a positive,non constant function and differentiable function such that

f’(x)(first deriative)<2f(x) and f(1/2)=1

Then the value of $\int_a^b$ a=1/2,b=1

lies in the interval

A (2e-1,2e)

B (e-1,2e-1)

C (e-1/2,e-1)

D (0,e-1/2)

Multiple correct

Please answer quickly

Gaganpreet Singh , 11 Years ago

Grade 12th pass

2 Answers

Arun Kumar

$f(1/2)<f(1)<c*e^{2x} \\=>1<f(1)<c*e^2\\ \\\\\\\\ f(x)<c*e^{2x}\\ =>\int_{a}^{b}f(x)<c*(e^2-e)/2 \\\\ f(1/2)<ce=>1<ce=>-1>-ce using \,this \\\int_{a}^{b}f(x)<c*(e^2-e)/2=ce(e-1)/2<(e-1)/2$

so D,B

Arun Kumar

IIT Delhi

Askiitians Faculty

Approved

Last Activity: 11 Years ago

Gaganpreet Singh

Please answer my one more question in analaytical geometry

Thanks

Last Activity: 11 Years ago

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Integral Calculus> Let f:[1/2,1] R be a positive,non constan...

Let f:[1/2,1] R be a positive,non constant function and differentiable function such that f’(x)(first deriative)<2f(x) and f(1/2)=1Then the value of a=1/2,b=1 lies in the intervalA (2e-1,2e)B (e-1,2e-1)C (e-1/2,e-1)D (0,e-1/2)Multiple correctPlease answer quickly

Gaganpreet Singh , 11 Years ago

Arun Kumar

Gaganpreet Singh

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Let f:[1/2,1] R be a positive,non constant function and differentiable function such that
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Then the value of $\int_a^b$ a=1/2,b=1
lies in the interval
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