Consider the figure below. f(x) = 2x – x2 g(x) = x2 - 6x 81x) -10...
Consider the following. The x y-coordinate plane is given. A horizontal line, a curve, and a shaded region are graphed. The horizontal line labeled f(x) = 25 crosses the y-axisat y = 25. The curve g(x) = x2 enters the window in the second quadrant, goes down and right becoming less steep, changes direction at the origin, goes up and right becoming more steep, passes through (5, 25) crossing the horizontal line, and exits the window in the first quadrant....
9. If f(x) = x2 - 6x + 2 and g(x) = -2x, find a. f.g(2) b. g•f(x)
Consider the following. у y=x (1,1) х 2 4 6 10 -2 x = 8 -4 y = 2 - x -6 -8 (a) Form the integral that represents the area of the shaded region. dx (b) Find the area of the region. (Give an exact answer. Do not round.)
1. .] For the following function f(x)= x* – 2x - 5 Determine the Inflection Points ONLY 2. For the given sketch of y i) Find the intersection points A, B and C. (Do not Estimate!) ***2, y =x +2; ii) Determine the shaded area enclosed between the given two curves y =*+2, y=x+2
1. .) For the following function f(x)= x4 – 2x - 5 Determine the Inflection Points ONLY 2.. For the given sketch of y = :) Find the intersection points A, B and C. (Do not Estimate!) +2, y=x+2= ii) Determine the shaded area enclosed between the given two curves -*+2, y =x +2
2. [8 pts] Consider the region R enclosed by the graphs of functions f(x) = 2 – 22 – 2x + 3 and g(x) = -2 +3 + 5 with points of intersection (-1,3) and (2,3), as shown in the figure. (a) Set up but do not evaluate the integral that repre- sents the volume of the solid resulting from revolving the region R about the vertical line r = 3. NA (b) Set up but do not evaluate the...
consider the differential equation dy/dx = -2x/y. find the particular solution y = f(x) to the guven differential equation witht the intial condition f(1)= -1 umowed for this question. D Consider the differential equatio find the particular solution y = f(x) to the given differential equation with the initial condition f(1) = -1 46) = -1 Hy=f2 xdx 17 2 + C = -x +C (b) (9.6) be the region in the first quadrant bounded by the graph of y...
Find all values of x satisfying the given conditions. f(x) 2x-4, g(x) = x2-6x + 20, and (fo g)(x) = 20 The values of x satisfying the given conditions are (Use a comma to separate answers as needed.)
Consider the vector field F(x, y, z) -(z,2x, 3y) and the surface z- /9 - x2 -y2 (an upper hemisphere of radius 3). (a) Compute the flux of the curl of F across the surface (with upward pointing unit normal vector N). That is, compute actually do the surface integral here. V x F dS. Note: I want you to b) Use Stokes' theorem to compute the integral from part (a) as a circulation integral (c) Use Green's theorem (ie...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...