3x +2 <0 and 4x -320
Find Var(2X-Y) Two random variables X and Y are i.i.d. and their common p.d.f. is given by f )- c(1+r) if 0 <r < 1. otherwise. f(3) = 10
Solve the linear programming problem by simplex method. . Minimize C= -x - 2y + z. subject to 2x + y +2 < 14 4x + 2y + 3z < 28 2x + 5y + 5z < 30 x = 0, y>02 > 0
2. (5) Solve each of the following 2) (r+7)?(x-3); <0 b) 2x +3r-11x 26
7 Consider the inner product space Co. 11 with the inner product defined by < 2,9 >= ( ( (x) g(x) dx (a) Show that f(x) = 1 and g(x) = 2x - 1 are orthogonal (b) Find ||g(2)|| (e) Find the distance d(f(x), g(x)) between f(x) and g(x)
Evaluate the function for the given value of x. 1-2x-5, {/x-7). for x<-1 for -1 <x<1 for x21 19, Find f(-1) undefined -8. -3 8.
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
cos x + cos 2x cos 3x+ cos 4x 0, is a) 3 c) 7 b) 5 d) 9 Let tan-1 y = tan, + tan-1 ( tan-1 (-Zr where |x| < + v/3 Then a value of y is 1-3z2 1-32 1 + 3z2 1+3 If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to tower, are 300 450 and 60 respectively then the ratio,...
(-2<x<3 21 Graph the feasible region for the system-15y 35 (2x + y<6
7. Let V = P2-{polynomials in x of degree 2 on the interval o <エく1) and let H span(1,2}, Find the vector in H (i.e., the linear function) that is closest to a2 in the sense of the distance