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345gq private CS/APR 2006/MAT235 UNIVERSITI TEKNOLOG! MARA FINAL EXAMINATION slide by COURSE CODE EXAMINATION TIME CALCULUS II FOR ENGINEERING MAT235 APRIL 2006 3 HOURS INSTRUCTIONS TO CANDIDATES 1. 2. 3. 4. 5. This question paper consists of five(5) questions. process ALL questions. redeem your answer to each question on a bare-assed page. Do not bring all material into the enquiry room unless permission is given by the Invigilator. Please infract to make sure that this examination get hold of consists of: i) the Question makeup ii) an Answer Booklet - provided by the skill DO NOT caper THIS PAGE UNTIL YOU ARE TOLD TO DO SO This examination paper consists of 4 printed pages © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL 2 CS/APR 2006/MAT235 QUESTION 1 rate [sec 5 xsinx dx. o (4 marks) a) b) Integrate f e x cos2x dx by victimisation the appropriate method. (7 marks) c) pass judgment f J - d x , by usi ng the method of partial(p) fraction. x(x-1)2 (8 marks) QUESTION 2 a) Approximate the take to be of (0.503)(1.004)2 using total derivative. (5 marks) b) ds Given s = 3 y 2 z 3 , y = 3x 2 + 2, z = V x - 1 , f i n d when x = 2 using the range rule. dx (6 marks) c) Evaluate the following integral 3 x2 Inz J | 1 x Jxe y dydzdx.

0 (8 marks) © Hak Cipta Universiti Teknologi MARA CONFIDENTIAL CONFIDENTIAL CS/APR 2006/MAT235 QUESTION 3 f X a) Use trigonometric switch to integrate j . x 4. ^ + 9 =dx (5 marks) b) If y(1 + x 2 ) ^ = 2x(1-y 2 ).prov ethat dx (1 + x 2 ) 2 ( 1 - y 2 ) = A whe! re A is constant. (7 marks) c) Solve the differential equation y - y x 2 + y 2 dx - x dy = 0 (9 marks) QUESTION 4 a) Solve the second order differential equation 2y + 3y + y = 2e _ t +1 (10 marks) b) A ice chest ab initio contains 200 liter of pure water. Then at condemnation t = 0 brine containing 5 gm of season per liter of water is allowed to enter the tank at the...If you unavoidableness to get a full essay, order it on our website: OrderCustomPaper.com

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