1) Given a continuous function g satisfying 90(9)ds = 33 and fo(9)ds = 31. Compute 5...
4. f(x) is a continuous function on [0, 1] and So f (x)dx = a, where a is constant. Evaluate the following double integral f(x)f(y)dydx. (Hint: Change the order of the integration and use the property of the double integral, so that you can apply Fubini's theorem.)
Consider the following initial-value problem. 5 f'(x) f(1) = 17 Integrate the function f'(x). (Use C for the constant of integration.) f'(x) dx Find the value of C using the condition f(1) = 17. с State the function f(x) found by solving the given initial-value problem. f(x) Consider the following. |--145 – 03 +49) du Simplify the integrand by distributing u to each term. SO Jau du x Find the indefinite integral. (Use C for the constant of integration.) 6...
In this question, we ask you to solve the differential equation dy (3x-6)2-(2y-s) dx satisfying the initial condition 4.1 (1 mark) Hopefully, you have observed that the d.e. is separable. Thus, as a first step you need to rearrange the d.c. in the form for appropriate functions fy) and g(x) Enter such an equation, below y) dy-g(x) dx Note. The differentials dx and dy are simply entered as dx and dy, respectively separated d.e You have not attempted this yet...
0.09/1 points Previous Answers SCalcET8 5.3.002. Let g(x)-f(t) dt, where f is the function whose graph is shown (a) Evaluate g(x) for x 0, 1, 2, 3, 4, 5, and 6 g(0)0 9(2)-8 g(3)-( 20 9(4)- 9(5) 9(6) ) g(6)- (b) Estimate g(7). (Use the midpoint to get the most precise estimate.) 9(7)- (c) Where does g have a maximum and a minimum value? minimum x= maximum x= (d) Sketch a rough graph of g. 7 83 gtx ry again....
(1 point) Let [ f(z)dx=-13, 5° f(x) dx = 3, $*g(x) dx = 6, §*9(a) dx = 1, J2 Use these values to evaluate the given definite integrals. a) ["{$(2) + 9()) dx = 6 .) – g(x)) dx = * (31(2) + 29(2) de = (af(x) + g()) dc = 0. d) Find the value a such that a=
Given the function ry g(x, y) = g(x, y) lim (x,y)(0,0) a. Evaluate iii. Along the line y i. Along the x-axis: x: iv. Along y x2: ii. Along the y-axis: g(x, y) exist? If yes, find the limit. If no, explain why not. b. Does lim (r,y)(0,0) c. Is g continuous at (0,0)? Why or why not? d. The graphs below show the surface and contour plots of g (graphed using WolframAlpha). Explain how the graphs explain your answers...
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that is defined on a region D that contains C and f(x,y) < M for all (x, y) E D. Show that f(x, y)ds 3 Me Hint: Use the following fact from single variable calculus: If f(x) g(x) for a KrS b, then (x)dJ() dr. Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that...
(-5,2) (-2,-1) Graph of g The continuous function g has domain -5 < x < 2. The graph of g, consisting of two line segments and a semicircle, is shown in the figure above. The graph of g has a horizontal tangent at x = -1. Let h be the function defined by h(x) = S-29(t)dt for -5 < < 2. (a) Find the x-coordinate of each critical point of h on the interval -5 < x < 2. (b)...
At what points is the following function continuous? x#9, x# - 9 x3 + 729 x² - 81 - 13.5, f(x)= x = -9 7, x= 9 Choose the correct answer below and, if necessary, fill in the answer box to complete your che O A. At all real numbers except at x = (Use a comma to separate answers as needed.) OB. Only at x = (Use a comma to separate answers as needed.) O C. At all real...
2 6 3 -2 5 -1 8 3 13 9 f(x) The function f is continuous on the closed interval [2, 13) and has values as shown in the table above. Using the intervals [2, 3]. [3, 5]. [5, 8), and [8, 13), what is the approximation of " f(x) dx obtained from a left Riemann sum? (A) 6 (B) 14 (C) 28 (D) 32 (E) 50