Determine whether the function shown is continuous over the interval (-6,6). Ay 6- 4- 2 y...
4. The function f is continuous on the closed interval (-2, 1). Some values of f are shown in the table below. --2 f(x) -3 -1 0 1 7 k3 The equation f(x) = 3 must have at least two solutions in the interval [-1,1) if k = a. 1 b. C. 2 CONN NICO d. 5. If k(r) is a continuous function over the interval (-2, 4) such that k(-2) = 3 and k(4) = 1, then k(2) 0...
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find 2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
In the following exercises, find the value(s) of k that makes each function continuous over the given interval. 145. f(x) = $3x + 2, x<k 12x – 3, k < x < 8 3 153. Apply the IVT to determine whether 2* = x has a solution in one of the intervals [1.25, 1.375] or [1.375, 1.5]. Briefly explain your response for each interval. Determine whether each of the given statements is true. Justify your response with explanation or counterexample....
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др
Suppose that a continuous function f has a derivative f' whose graph is shown below over the interval (4, 13). y=f'(x) 1 2 3 4 5 6 7 8 9 10 11 12 13 (a) Find the interval(s) over which f is increasing. (Enter your answer using interval notation.) (4, 6)U(7, 9) U (11, 13) Find the interval(s) over which f is decreasing. (Enter your answer using interval notation.) (6, 7) U (9, 11) (b) Find the x-value(s) where f...
By inspecting a graph of y = sin x, determine whether the function y = sin x is increasing or decreasing on the interval The function y=sin x is on the interval By inspecting a graph of y = sin x, determine whether the graph is concave up or concave down on the interval (1,21). The graph is on the interval (1,21). Minimize f(x,y)= x2 + xy + y2 subject to y = 20 without using the method of Lagrange...
Suppose that a continuous function f has a derivative f' whose graph is shown below over the interval (1, 10). y=f'(x) 1 2 3 4 5 6 8 9 10 (a) Find the interval(s) over which f is increasing. (Enter your answer using interval notation.) Find the interval(s) over which fis decreasing. (Enter your answer using interval notation.) (b) Find the x-value(s) where f has a local maximum. (Enter your answers as a comma-separated list.) x = Find the x-value(s)...
Sketch a possible graph of a function that satisfies the conditions below. Determine whether fis continuous at x = 1. f(1) = 2; lim f(x) = -2; lim f(x) = 2 x=1 *1* Choose the correct graph below. OA. B. OC. D. ro х X х -5 5 -5 5 -5 5 -5 5 Is f(x) continuous at x = 1? No оо Yes
Determine whether the Mean Value Theorem applies to the function fx) -2-x2 on the interval [-2.1 . If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem. a. Choose the correct answer below O A. No. because the function is differentiable on the interval (-2.1), but is not continuous on the interval [-2.1 O C. No. because the function is not continuous on the interval [ -2.1). and is not differentiable on the interval (-2.1)...
determine whether there is a value for c making the function continuous everywhere. If so, find it. If not, explain why not cy 19. f(a, y) 5 y x > 3 cy 19. f(a, y) 5 y x > 3