one-to-one function f(x) satisfies f(0) = 0 and f(x) 0 If ∫a0f(x)dx = Afor a > 0, find an expression for ∫a0f( )f -1(x)dx.

If f(x)𝑓(𝑥) is a probability density function of a continuous random variable, then ∫∞−∞f(x)dx=∫−∞∞𝑓(𝑥)𝑑𝑥=  ?a.1b.undefinedc.Insufficient datad.0

If the function f(x) = ax3 – 6x2 + 11x – 6 satisfies conditions of Rolle’s theorem in [1, 3], then the value of a must be ________.

Consider the function f : R → R defined by f (x)=1 if x∈ Q, f (x)=0 if x∈ R/Q, where is f continuous? be sure to prove your assertion

Find f.f '''(x) = cos(x),    f(0) = 2,    f '(0) = 6,    f ''(0) = 5f(x) = 6x+1+cos(x)

Find the linear and quadratic approximations to the following function about x = 0 :f (x) = (1 + x)5and so find approximations for 1.055