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 and cos B-cos C as shown below
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=(a+b)/2; which 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..https://brainly.in/question/41188750
2) Verify Cauchy's mean value theorem for the function sin x and cos x in the interval [0,π/2]https://brainly.in/question/144129
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