Let a be a positive constant number. For a positive integer n, define a function In(t) by I_n(t)\equal{}\int_0^t x^ne^{\minus{}ax}dx. Answer the following questions.
Note that you may use \lim_{t\rightarrow \infty} t^ne^{\minus{}at}\equal{}0 without proof.
(1) Evaluate I1(t).
(2) Find the relation of I_{n\plus{}1}(t),\ I_n(t).
(3) Prove that there exists limt→∞In(t) for all natural number n by using mathematical induction.
(4) Find limt→∞In(t). calculusintegrationfunctionlimitinductioncalculus computations