CALCULUS PAPER - JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY UNIVERSITY EXAMINATIONS 2017\/2018 SECOND YEAR FIRST SEMESTER EXAMINATION FOR

# CALCULUS PAPER - JOMO KENYATTA UNIVERSITY OF AGRICULTURE...

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JOMO KENYATTA UNIVERSITY OF AGRICULTURE AND TECHNOLOGY UNIVERSITY EXAMINATIONS 2017/2018 SECOND YEAR FIRST SEMESTER EXAMINATION FOR BACHELOR OF SCIENCE IN MECHANICAL AND MARINE ENGINEERING SMA 2277: CALCULUS III DATE: DECEMBER 2017 TIME: 2 HOURS INSTRUCTIONS: Answer question ONE and any other TWO questions QUESTION ONE (COMPULSORY)[30 Marks] a)Determine if f(x)(x39x2+19x35)(x7)is continuous at x=7 = (2 marks) b)Evaluate the limitlimx→0(exln(1ex))(2 marks)c)Determine all the number cwhich satisfy the conclusion of Rolle’s Theorem for the givenfunction and interval, f(x)=x22x8,on[1,3](3 marks)d)State the mean value theorem and verify it for f(x)=x3+2x2x ,on[1,2(4 marks)e)Test for convergence of the series =1(3n)!n!(2n)n(4 Marks)f)Find the radius and interval of convergence of =0(x+1)n2n(n2)(3 Marks)g)By changing the order of integration evaluate 1xxx dy dx(4 Marks) ] n n 0