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- Find the minimal distance between the point (3, 9) and the curve of the function f(x) = 9 − x^2Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which consists of line segments and semicircles of radius 3 connecting the points (−8, 0), (−6, 6), (0, 6), (6, 6), (8, 0). What is the multipart formula for y = g(x) when -6 <= x <= 0 and when 0 <= x <= 6?Let C be the curve y=4.5ln(20.25−x2)y=4.5ln(20.25-x2), for −3.6≤x≤4.1-3.6≤x≤4.1. A graph of y follows.
- #8 Find a function r(t) that describes the line passing through P(8,7,2) and Q(3,6,7). r(t)={-5t+8, , }, forLet S be the graph of f(x, y) = x2 + y2 - 2x + y for(x, y) ∈ D = {(x, y) : x2 + y2 ≤ 4 and x + y ≥ 0}. Let C1 be the curve along the edge of the graph of fover the straight edge of D – starting in the secondquadrant and ending in the fourth quadrant of D • Let C2 be the curve along the edge of the graph of fover the circular edge of D – starting in the secondquadrant and ending in the fourth quadrant of D. Let F(x, y, z) = ⟨x, y, y z⟩ Compute R: C1 F¯ · dr¯.Consider an F-curve with d f = (2, 14). Identify the degrees of freedom for the denominator.
- Use the following information to sketch the graph of y=f(x) * f is increasing at (-♾, -2] U [0, ♾) f(x) is decreasing at [-2,0]* local minimum is -4 at x= 0 local maximum is 0 at x=-2 * x intercept is (1,0), (-2,0) y intercept is (0,-4) * inflection point is (-1,-2) * f is concave up at (-1,♾) f is concave down at (-♾,-1)1)if the line x=0 is a vertical asymptote of y=f(x) then the function is not defined at x=0 true or false.Suppose f (x, y) = 25 −4x2−3y2. Calculate both fx(1, −1) and fy(1, −1). Sketch (by hand, or,better, using software of your choice) some level curves for the function f . Use these sketches tointerpret your answers as slopes.