Multivariable Calculus ADP/BS 2 Semester/Term UOS — University of Sargodha 2025

University of Sar odha coat 5 ADP/BS 2" Semester (p-24) Examination 0 5101 Ber Jus (MATH: ject: T Paper: Multivariable Calcu 4 Subject: CS/SE/L Mul Maximum Marks: 60 Time Allowed: 02:30 Hours : . : ioctive part. Note: ~ Objective part is compulsory. Attempt any three questions from subjective P Objective Part (Compulsory) CAN MC Q.1. Write short answers of the following in 2-3 lines each on your answer S Sa Lr 5 . oz ih Find = if yz—lnz=x+y ii. Find f3a,a)if f(x,y) = x + xy3 se A _ Gem) s iL it fe iii. Find J(w,v) = To5) ifx =3(u+ 2v),y =; (u v) iv. Evaluate: [ 5 J xye*dydx v. Evaluate: L(tsin(5t)) - vi. Find h(t) If H(S) = — by convolution theorem vii. Find the Maclaurin series for ix nL 1—x viii. Evaluate: lim = : xy)—»(3B1) x-y x+y ix. Use polar Coordinate to evaluate [f, x?dA where R is the region inside circle. x>+y%2=9 x. Use cylindrical coordinate is find volume of the solid bounded by z = 0 and z = 4 — 72 Vi-—. 2 xi. Evaluate: fi J 12° J1— x2 — y2dydx xii. Define the Fourier Sine transformation. Subjective Part (3*12) 12) Find the derivati iC 7) = yz AN : Q : ; bl oh ive of f(x,y,2) = cos(xy) +e”? + In(zx) at P (no, 3) BL ditestion of b) Find the Linearization of f(x,y, 2) = T2& =). E z TE Q.3. Find the radius and interval of Convergence of series Yin (x n series converges. n=0 (X + 5)", for what value of x does the Q.4. Find the Maximum and Minimum values of 3x — y + 6 subject : Q.5. Find the volume of the region bounded bythe elliptical pam : Gn x? +y2 = 4, square R:0