Verify Cauchy's mean value theorem for the
function sin x and cos x in the interval [a, b]
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Step-by-step-Explanation:
Given : sin x and cos x
To find: Verify Cauchy's mean value theorem for the function sin x and cos x in the interval [a, b]
Solution:
Cauchy's mean value theorem:
Let f(x) = sin x
and g(x)=cos x
Put the function and first order derivative in the formula
Put the formula for sin B-sin C=
put these formulas in eq1
or
Cancel common terms from numerator and denominator
c lies in the closed interval [a,b].Thus, Cauchy's mean value theorem holds.
Final answer:
c lies in the closed interval [a,b].
Thus, Cauchy's mean value theorem holds and have been proved.
Hope it helps you.
To learn more:
1)
Chapter : complex..
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2) Verify Cauchy's mean value theorem for the function sin x and cos x in the interval [0,π/2]
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