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Verify Rolle’s theorem for each of the following functions on indicated intervals : f(x) = sin x + cos x – on
Asked by Topperlearning User | 04 Aug, 2014, 04:16: PM

Since sin x and cos x are everywhere continuous and differentiable. Therefore, f (x) = sin x + cos x – 1 is continuous on  and differentiable on

Also, f (0) = sin 0 + cos 0 – 1 = 0 and
\                 f (0) =
Thus, f (x) satisfied conditions of Rolle’s theorem on  Therefore, there exists c ε  such that f ¢ (c) = 0
Þ cos x – sin x = 0 Þ sin x = cos x Þ tan x = 1 Þ x =
Thus, c =  such that f ¢ (c) = 0
Hence, Rolle’s theorem is verified
Answered by | 04 Aug, 2014, 06:16: PM

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