Analytical Geometry/Calculus and Analytic Geometry BS 1 Semester/Term University Of Sargodha (UOS) 2024

University of Sargodha BS 1* Term Examination 2024 Paper: Calcules & Analytical Geometry (MATH-101/ MATH-2213) Maximum Marks: 60 Subject: CS/IT/SE Time Allowed: 02:30 Hours Note: Objective part is compulsory. Attempt any three questions from subjective part. Objective Part (Compulsory) Write short answers of the following in 2-3 lines of each on your answer sheet. jck Define hyperbota Win are eylindent condimates? Change the rectangulag polinute (0, -1, -D) to eylindrical ecordinate: What is a connection between the define legal j (se)ds and the indefinite integral J F(x) de? What is jerk? Why the jetk during free fall is zero? i Find the linearization 1(x) of F(x) = x+! at a = 1. (2*12) Q.2. 0.3. State Mean Value Theorem. If I and g are both differentiable, then find 1 2(x)] deg(0) What is a vector function? How do you find its derivative and its integral? then Find the domain of / Define continuous extension g(3) in a way that extends g(x) = (x? - 9)/(x - 3) to be continuous at x = 3. Subjective (3"12) (a) If f(x) = 2x'- 3x7-12x, then ( Find inflection point (ii) Find the intervals where the function is concave up or concave down. Do Find *2 as as a function of tifx = t+, andy = t -l (a) Use Newton Rapshon Method to approximate up to four places of decimal a root of the e' - 3x = 0 with x, =0. (6) Calculate 15(0)x 5(0) by asing formula, where (0) = 3 secri- + Ince de 3(1)= 4 - sick. (Le 5(0) - 2x-l i/1