Pre Calculus BS Computer Science 2 Semester/Term PU — University of the Punjab 2022

UNIVERSITY OF THE PUNJAB B.S. in Computer Science Second Semester - Spring 2022 Subject: Pre-Calculus-II Paper: MD-002 THE ANSWERS MUST BE ATTEMPTED ON THE ANSWER SHEET 1. Solve the following questions. (15x2=30) (i) Solve (2,6) + (3,7). (ii) Simplify (-i)^19. (iii) Separate f/(1+i) into real and imaginary parts. (iv) Find the 13th term of the sequence x, 1, 2-x, 3-2x, ... (v) If a, b, c, d are in geometric progression (sequence), show that a-b, b-c, c-d are in geometric progression. (vi) Evaluate 12P5 and 20C17. (vii) A die is rolled, What is the probability that the dots on the top are greater than 4? (viii) Using Binomial Theorem expand (a+2b)^5. (ix) Discuss the continuity of f(x) = (x^3-1)/(x-1) at x=1. (x) Find dy/dx of y = (a+x)/(a-x). (xi) Determine the intervals in which f(x) = x^2+3x+2 is increasing or decreasing for the domain x ∈ (-4,1). (xii) Find the area between x-axis and the curve y = x^2+1 from x=1 to x=2. (xiii) Simplify the indefinite integral ∫ x^2/(4+x^2) dx. (xiv) What is meant by relative maxima of a function? (xv) Simplify ∫_0^1 (x^3+1) dx. Solve the following questions. (6x5=30) (2) Simplify (-1/2 + √3/2 i)^3. (3) The sum of 9 terms of an arithmetic progression is 171 and its 8th term is 31. Find the series. (4) If y = 2/3 x + 4/9 x^2 + 8/27 x^3 + ... and if 0 < x < 3/2 then show that x = 3y / 2(1+y). (5) Determine whether lim x->2 f(x) and lim x->4 f(x) exist, when f(x) = { 2x+1 if 0<=x<=2; 7-x if 2