nts) Suppose that f(x) is continuous. The table below shows where f'(a) and f"() are positive and negative....
Suppose that f(x) is a continuous function on (2,7), positive on (2,5) and negative on (5,7) If f(x) dx = 3, then find If(x) dar. () dx = 11 and Ś "S" ) dr = = -3, Ls =) dr = 5, (b) Suppose that f is an even and integrable function. If then find Lºs(z) dr.
Problem 4. (6 pts) (a) Suppose that f(x) is a continuous function on 2,7], positive on (2,5) and negative on (5, 7). « [ r(a) dr = 11 and ſsaw) dr = 3, then ind ſis(2) dr. .10 f(x) (b) Suppose that is an even and integrable function. If "L" 3, . f(x) da = 5, then find L" (a) dr.
Let f(x) k sin(kx), where k is a positive constant (a) Find the area of the region bounded by one arch of the graph f and the x -axis. b) Find the area of the triangle formed by the x -axis and the tangents to one arch nts to one arch of f at the points where the graph of f crosses the x -axis
Let f(x) k sin(kx), where k is a positive constant (a) Find the area of...
14. Suppose that f(x) is continuous on (60,-) Given the graph y = f'(x) below, find the following: y = f'(x) In (None may be an answer): Find the number lines of f'&f" 1. relative maximumat x= 2. relative minimum at x= 3. The graph of y=f(x) has points of inflection at x= -&x= (Enter a number from smallest to largest x-value.)
3. Suppose lim s(a) dr = co, where f(a) is a positive, decreasing and continuous function. Which of the following statements is true about the series f(n)? Choose one. n=1 *Please write the letter of your choice. (a) The series converges too. (b) The series converges, but not necessarily to o. (c) The series diverges. (d) The given information is not enough to determine if the series converges or diverges.
6.59. Let f be a continuous function on [a, b]. Suppose that there exists a positive constant K such that If(x) <K for all x in [a, b]. Prove that f(x) = 0 for all x in [a, b]. *ſ isoidi,
Draw a graph to match the description given. F(x) has a positive derivative over (-0,1) and (6,9) and a negative derivative over (1,6) and (9,00). Which of the following graphs matches the description? ОА. OB. O C. OD. @ 8
(7 points) Suppose X and Y are continuous random variables such that the pdf is f(x,y) xy with 0 sx s 1,0 s ys 1. a) Draw a graph that illustrates the domain of this pdf. b) Find the marginal pdfs of X and Y c) Compute μΧ, lly, σ' , σ' , Cov(X,Y),and ρ d) Determine the equation of the least squares regression line and draw it on your graph.
(7 points) Suppose X and Y are continuous random...
need help please with clear answers
6. (a) Below are the graphs of f'(x) and f'(x). On well-labeled axes, draw a graph of f(x) which has these first and second derivatives. Explain why your answer is correct "(x) (b) Below is the graph of the function g. Using a table like the one next to the graph, indicate whether 9.9.g" are positive, negative or zero at each of the labeled points. g(x) Pointg g' g
5. Suppose X is a continuous RV modeled by f(x; a) =-e-le-al where-oo < x < 00, If a random sample of size n is drawn with n odd, show the MLE for α is the median of the sample.