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- Let G(u, v) = (5u + v, 30u + 13v) be a map from the uv-plane to the xy-plane. Find the image of the line through the points (u, v) = (1, 1) and (u, v) = (1,–1) under G in slope-intercept form. (Express numbers in exact form. Use symbolic notation and fractions where needed.) equation:2) The contour map of f(x, y) is shown below. Use it to find fx (1,3) 10 10 8 8 6 =2 6 0 x=2 6 8 10Sketch the graph of f(x.y) = 4x +y + 1. State the domain and range of the function. Which of the following surface graphs represents f(x,y) = 4x + y? + 1? OA. Ов. OC.
- Let A = {4, 5, 7} and B = {x, y}. Let p1 and p2 be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b) A ✕ B, p1(a, b) = a and p2(a, b) = b. (a) Find p1(4, y) and p1(7, x) What is the range of p1? (Enter your answer in set-roster notation.) (b) Find p2(4, y) and p2(7, x). What is the range of p2? (Enter your answer in set-roster notation.)Find the domain of the function f(x, y) = In(3x? – 2y + 1). The set of all ordered pairs (x. y) for which: - 3x2 (A) y (F) y s 1+ (G) y 2 * (H) y > 1+ 3x2 (Н) у >The points in the left column are on the graph of y = f(x), Match the point on the left to the point where it is located if each point is shifted left 4 units and up 2 units. O Hold and drag to reorder (0, – 3) = (-5, – 2) (1, – 4) -4, – 1) (-1,0) = (0,3) (4,5) -3, – 2) = (-3,2) = (-5,2) = (0,7) = (-4,1) Submit
- Figure 4 shows the contour map of a function f (x, y) together with a path r(t) in the counterclockwise direction. The points r(l), r(2), and r(3) are indicated on the path. Let g(t) = f (r(t)). Which of statementsSelect the option that gives a list of the stationary points of the function ƒ(x, y) = x³ – 3x² − 3xy² + 18xy – 24x – 1. Select one: O (0, 2), (0, 4), (1, 3) (1, 2), (1, 4), (0, 3) (1, 4), (0, 3) (2, 0), (4, 0), (3, 1) O (2, 1), (4, 1), (3, 0)
