Question

verify the cauchy's mean value theorem for 1/x in [1,e]​

Answer 1

Step-by-step explanation:

have Cauchy’s mean value theorem Thus the theorem is verified. (ii) We have Cauchy’s mean value theorem Clearly both f (x) and g (x) are continuous in [0, π/2] and differentiable in (0, π/2). Therefore from Cauchy’s mean value theorem ∴ f (x) and g (x) are continuous in [a, b] and differentiable in (a, b) and also g′ (x) ≠ 0 ∴ From Cauchy’s mean value theorem Hence Cauchy’s theorem holds good for the given functions.Read more on Sarthaks.com - https://www.sarthaks.com/354101/verify-cauchys-mean-value-theorem-for-the-following-pairs-of-functions