Pre Calculus ADP/BS 2 Semester/Term government university FSA 2025

University of Sarg9=—== odha ADP/BS 2" Semester (F- amination 20% H-5101 TH- Subject: EAT Paper: V riable Calculus ) 5 . CSIS aper: M Maximum Marks: 60 Time Allowed: 02:30 Hours \ i 0) tive part. oui Objcin part is compulsory. Attempt any thee questions from subjective P: a) 0 Objeid Prt (Compulsory) C SOF (2*12) Q.1. Write short answers of the following in 2.3 lifies each on your answer sheet No i. Find fa ifyz—Inz=x+y Ov ii. Find f(3a,q)if f(x,y) = x* + xy* iii. Find Juv) = = ifx=3(u+2v)y=3u-"v) iv. Evaluate: [ = J xyexdydx v. Evaluate: L(tsin(5t)) + vi. Find h(t) If H(S) = re by convolution theorem vii. Find the Maclaurin series for = ite : xi-y? viii. Evaluate: Es = x%y ix. Use polar Coordinate to evaluate [f, x?dA where R is the region inside circle. x+y: =9 x. Use cylindrical coordinate is find volume of the solid bounded by z = 0 and z = 4 — 72 3 xi. Evaluate: [J f) TF [Tx —yidydx y xii. Define the Fourier Sine transformation. | Subjective Part (3*12) Q2. a) Find the derivative of f(x,y,2) = cos(xy) + e’” + In(zx) at P (103) in the direction of U=i+2j+2k a b) Find the Linearization of f (x,y,z) = — at (=). Q.3. Find the radius and interval of Convergence of series Yo n eins converse series 3g (x + 5)" | for what value of x does the Q4. Find the Maximum and Minimum values —y +6 subject to : Q.5. Find the volume of the region i Welz 2 ¢ amo x 2+y?=4, square R: 0