Answer :

Condition (1):


Since, f(x)=e-x (sinx-cosx) is a combination of exponential and trigonometric function which is continuous.


f(x)= e-x (sinx-cosx) is continuous on .


Condition (2):


Here, f’(x)= e-x (sinx + cosx) - e-x (sinx – cosx)


= e-x cosx which exist in .


So, f(x)= e-x (sinx-cosx) is differentiable on


Condition (3):


Here,


And


i.e.


Conditions of Rolle’s theorem are satisfied.


Hence, there exist at least one such that f’(c)=0


i.e. e-c cos c =0


i.e. cos c = 0


i.e.


Value of


Thus, Rolle’s theorem is satisfied.


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