Test Paper - Applied Maths - Mumbai University - Chemical Engineering -3rd Semester - 2008, Study notes of Mathematics

Download Test Paper - Applied Maths - Mumbai University - Chemical Engineering -3rd Semester - 2008 and more Study notes Mathematics in PDF only on Docsity!

SE COM eC Foti AEE JC ear), © eC, OF , g }Sub: Apples Podhomedies -0 3]1 Joa (ORY } Con. 5762-07. (REVISED COURSE) CD- 6768 (3 Hours) [Total Marks : 100 N.B.: (1) Question No. 1 is compulsory. {2) Attempt any four questions from the remaining six. (3) All questions carry equal marks. (4) Use of Calculator's (Non-Programmable) is allowed. 1. (a) Ifft) st+1 02 Find L[f(t)] and L [#(t)] Prove that : f2 [3 3-x?" J_sj2 (x) = zl sinx + 2 { Under the mapping W = z show that the image of the hyperbola x? — y? = 1 a is hemniscale e = cos 2 o. d Using milne predictor-corrector formula. Find. y(1-4) given - =x? (i+y) and y(1) =1, y(1-1) = 1-233, y(1-2) = 1-548, y(1-3) = 1-979. Prove that J_p (x) = (-1)" Jn (x) where n is +ve integer. Prove that : L [f¢t)] andL [rat] L sinh 1 t sin Zt _18 _ § _ 2 2 2 (st+s241 d Using modified Euler's method. Find y(0-1) and y(0-2) given that = = x2 4y?, y(0} = 1 If f(z) is analytic function, Show that 2 2 2 init «fal =i" oe [ren] [rea] =i" [TURN OVER