f(x)=e^(x)cos x" on "[-(pi)/(2),(pi)/(2)]

f(x)=cos2x, interval [-(pi)/(4),(pi)/(4)]

Verify Rolle's theorem for the following functions in the given intervals and find a point (or point) where the derivative vanishes : f(x) = e^x cos x in [-pi/2,pi/2]

If f(x)=cos^(2)x*e^(tan x),x in(-(pi)/(2),(pi)/(2)) ,then

If f(x)=(e^(x)+e^(-x)-2)/(x sin x) , for x in [(-pi)/(2), (pi)/(2)]-{0} , then for f to be continuous in [(-pi)/(2), (pi)/(2)], f(0)=

If f(x)=(e^(x)+e^(-x)-2)/(x sin x) , for x in [(-pi)/(2), (pi)/(2)]-{0} , then for f to be continuous in [(-pi)/(2), (pi)/(2)], f(0)=

Verify Rolle's theorem for each of the following functions: (i) f(x) = sin^(2) x " in " 0 le x le pi (ii) f(x) = e^(x) cos x " in " - (pi)/(2) le x le (pi)/(2) (iii) f(x) = (sin x)/(e^(x)) " in " 0 le x le pi

If f(x)=e^(x)+int_(0)^(sin x)(e^(t)dt)/(cos^(2)x+2t sin x-t^(2))AA x in(-(pi)/(2),(pi)/(2)),then

Let f(x)={-2sin x for -pi<=x<=-(pi)/(2)a sin x+b for -(pi)/(2)

If f(x) =sin x +log_(e)|sec x + tanx|-2x for x in (-(pi)/(2),(pi)/(2)) then check the monotonicity of f(x)

If f(x) =sin x +log_(e)|sec x + tanx|-2x for x in (-(pi)/(2),(pi)/(2)) then check the monotonicity of f(x)