Multivariable Calculus ADP/BS 2 Semester/Term University Of Sargodha (UOS) 2025

PER Bad SN IC ga Bp SLT p TET University of Sargodha Subject: CS/SENT aper: Multivariable C H-510 Time Allowed: 92:30 Hours Maximum Marks: 60 Note: 1 Objective part is compulsory. Attempt an) three questions from subjective part. Objective Part (Compulsory) C\ Q.1. Write short answers of the following in 2-3 lines each on your answer sheet. (2*12) i. Find o fyz—-Ilnz=x+y ax : X i Find f(3a,a) if f(x,y) 2 x° + xy° J A 3 ii, Find J(u, v) = =2d] if x = = (u + 2v),y==(u—v) iv. Evaluate: ji J : xye*dydx » Evaluate: L(tsin(5t)) vi Find h(t) If H(S) = — by convolution theorem vii Find the Maclaurin series for =z Pra FE Rp AE ) Bl a Hl on er Q.1. THER i 2 I. i. Find 3 if yz—Inz = =x+y oo ii. Find Ga, a) if [zx + xy? ii. Pld JG) = 3.55 IF = lu+2v)y=2@-v) iv. Evaluate: [| 4M xye*dydx » Evaluate: L(esin(5e)) vi. Find h(t)If H(S) = rr by convolution theorem vii. Find the Maclaurin series for > . vii. Evaluate: lim = | (xy)=(31) x-¥y i xy ] { ix. Use polar Coordinate to evaluate J I x?dA where R is the region inside ci 2 = ; x+y =9 Use cylindrical coordinate i is find volume of the solid bounded byz=0 yd z xi. Evaluate: [J [7 JT; —& —yRdyds we | xij Defi 56 1h Fouls Sine transformation. ‘Subjective Part (3*12) Q2 a) Find the derivative of f(x,y,2) = has fl + In(zx) at P(1, 0, 3 in the direction of U=i+2j+2k #5) Find the Linearization of f(x, y,2) = en at G5) Q3. Find and interval of Convergence of series Yi. (x +5)", converges. ini 6 subject to the constraint x? + y* =4.~ \Y the Maximum and Minimum values of 3x oB Find the volume of the region bounded by iptical paraboloid z = 16 — x? — y? — square R:0