Fundamentals Of Mathematics — DU B. Voc – Web Designing Previous Year Question Papers

(b) Let f(x) = elx/ Find the limit lim + (x) -1 7. Do the following parts: (9x2) (a) If: f(x) = |2x - 3|, then show that f is integrable on close interval [-1, 2] and hence evaluate 1. Do the following parts: (9x2) (a) Find the intervals in which f(x) =-2x2 - 4x +4 is increasing and the intervals on which f is decreasing. (b) Find the open interval on which f(x) = x + 2 sin x, E [O, 2u] is concave up and where it is concave down. Also determine points of inflection, if any. 2. Do the following parts : (9x2) (a)IF - (6 9) and ss - (fi d). show that ! (b) Use Cramer's rule to solve the linear system: Do the following parts: (9x2) (a) Let f(x) = Ix, find the domain and range of the function. (b) Examine the continuity of the function f (x) = , × #0 4. Do the following parts: (9x2) (a) Show that the function f(x) = |x-2| + 1 is continuous everywhere but not differentiable at x = 0. (b) Evaluate lim x→0 5. Do the following parts: (9×2) (a) Let us assume that F is a relation on set R real numbers define by Fy if and only if x - y is an integer. Prove that F is an equivalence relation on (0) 181 - 22 100 2) 4 and f(x) = x2-3x+2, show that f(A) = 0. 6. Do the following parts: (9x2) (a) Find all critical points of the function f(x) = x3 -