numerical analysis mechanical engineering, Exams of Numerical Methods in Engineering

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Princess Sumaya University for Technology Department of Basic Sciences Numerical Analysis (20333)- First Exam - Summer 2017 Instructor: Dr. Samia Bushnag Student's Name: cecccccccscsrecrsessesseneeeeeeesees Show your work! If insufficient work is shawn, full credit may not be awarded. Approximate your ahawers to four decimals places. (ROUNDING) J. (10 points) Let f(x) =32+sinzg—e™, x € [0,1] (a) (2 points) Show that f(x) has a root: in [6, Y). (b) (2 points) What is the lcast number of Bisection method iterations nceded to approximate the root of f(x) accurate to within 10-5. (c) (3 points) Apply Newton’s method two times to approximate the root of f(x) starting with x, =0. (d) (3 points) Apply the False Position method two times to approximate the root of f(z). os ; L Cle ® Qos e Choi) “Joo a-bL fis Se Shoe = RYT adlorfiy <0 By Let, ; Yee ent, eé Col) such Wat fterso = CL 0 xood SS Gon FOd= 34 cory eX L