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  3. answer all questions clearly and with detailed steps thank...

Question: answer all questions clearly and with detailed steps thank...

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answer all questions clearly and with detailed steps !

thank you :)!

2. (a) Let n > -1. Use integration by parts to express I(n + 1) / (ze-z) dz 0 in terms of Г(n) (Hint: For any n, LHospitals rule gives that rn → 0 as → oo.) (b) Hence evaluate the definite integral Tie given that 2 e (c) Use the fact that Γ( )-VF to calculate the integral 0 (d) Using the result in part (a), demonstrate that「(n + 1) = n! for any n E {1, 2, 3, 4, ) Assignment 2 Page: 2 of 5 MCD4500 Trimester 3 2018 (e) In fact, m-factorial for any m can be defined as m-「(m + 1)(you are not required to show this identity). Use this identity, part (a) and part (b) to find the value of (-)!

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