Exercise 5.4.1. Let Z~Nor (0, 1) and define X₁ = Z and X₂ = Z². Computer, y), TK (X₁, X₂)(X, X₂)

Find the constants m and 6 in the linear function y = f(x)= mx+ 6, such that f(1) = -2 and f(3) = 6. O a) m – 4, b = -6. O b) m = -4, b = 2. %3D c) m 2 O d) m =,b= . O e) None of these. Page 7 of 25 Previous Page Next Page

əz əz 3. Let z = x² + y³, x = 2st and y = s-t². Compute for and əx Ət

Example: Calculate the value of (aw/@x) at the point (x, y, z) = (2,-1,1) if:- w = x2 + y2 + z? z3 – xy + yz +y3 = 0 Assuming that x and y are the independent variables.

4.4. Suppose that u = (1,3) and v = (3, 1). (a) Sketch the points u + v, žu +v, and u + fv. (b) Draw the line of all linear combinations cu + dv with c+ d = 1.

Form 2 of the chain rule. Do the following problems: A. Let z = u² + v²; u = 2x + 7, v = 3x + y. Compute using the chain rule and evaluate it at (x, y) = (2,3). (Answ: = 98 ) əz Əx

Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find d. A-D e. A x B f. BxB g. AND' h. D'n (AUB)

Let y = U 4 + 5 U and u = = = x³ - 2x.

J1, 1), К(3, 2), L(4, 1) and M(6, 1), N (5, 2), P(2, 1) 3)

Given z = = f(x, y), x(u, v), y = y(u, v), with x(-1, 6) = 1 and y(-1,6) = 5, calculate z,(-1, 6) in terms of some of the X = values given in the table below. fx(-1,6) = r f,(-1,6) = px„(-1,6) = b y,(-1,6) = q fx(1,5) = 1 f,(1,5) = -5 x,(-1,6) = c y,(-1,6) = a %3D z, (-1, 6) =