Answer the following questions for positive integer n.
(1) Find the maximum value of f_n(x) \equal{} x^ne^{ \minus{} x} for x≥0.
(2) Show that \lim_{x\to\infty} f_n(x) \equal{} 0.
(3) Let I_n (x) \equal{} \int_0^x f_n(t)\ dt, find limx→∞In(x). calculusintegrationlimitfunctionderivativecalculus computations