Q. 174.0( 1 Vote )
Verify Rolle’s th
Since, f(x)=e-x sinx is a combination of exponential and trigonometric function which is continuous.
⇒ f(x)= e-x sinx is continuous on [0,π].
Here, f’(x)= e-x (cosx – sinx) which exist in [0,π].
So, f(x)= e-x sinx is differentiable on (0,π)
Here, f(0)= e-0 sin0=0
And f(π)= e-πsinπ =0
Conditions of Rolle’s theorem are satisfied.
Hence, there exist at least one cϵ(0,π) such that f’(c)=0
i.e. e-c (cos c – sin c) =0
i.e. cos c-sin c = 0
Thus, Rolle’s theorem is satisfied.
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