(1 point) Find the average value of f(x,y) = 2x + ey over the rectangle R...
10. Find the volume for f(x, y) = xy + ey over the rectangle in the xy-plane that has corners at (3,1) and (4,2).
Find the average value of f over the given rectangle. f(x,y) =4x2y, R has vertices (-2,0),(-2,5),(2,5),(2,0).
Find the average value of f over the given rectangle. f(x, y) = 2x2y, R has vertices (-5, 0), (-5, 4), (5, 4), (5,0). fave = _______
Find the average value of f(x, y) over the region Rwhere A is the area of R in the following equation. Average value - Ā J 1(x,y) dA f(x,y) = xy R: rectangle with vertices (0, 0), (7,0), (1, 2), (0, 2) Enter a number Submit Answer Practice Another Version
(1 point) Let R be the rectangle with vertices (0,0). (8,0). (8, 8), and (0,8) and let f(x, y)- /0.25ry. (a) Find reasonable upper and lower bounds for JR f dA without subdividing R. upper bound lower bound (b) Estimate JRf dA three ways: by partitioning R into four subrectangles and evaluating f at its maximum and minimum values on each subrectangle, and then by considering the average of these (over and under) estimates overestimate: Inf dA underestimate: JRfdA average:...
Find the average value, I^bar, of the function f(x, y) = 7(x + y)In x over the rectangle A = {(x, y): 1 graterthanequal x graterthanequal 5, 0 graterthanequal y graterthanequal 5}.I^bar = 7 (5 In 5 - 4) I^bar= 7(25/4 ln 5 + 4) I^bar = 7(4/25 in 5 - 4) I^bar = 7 (25/In 5 - 4) I^bar = 7 (25/4 In 5 - 8)
2. (25 points) Find the average value of f(x,y) = x + y over the first quadrant of the circle of radius 2 centered at the origin. x = cosey = r sin 8 dydx = r drde
Consider the vector field F(x, y) = (ey – ysin x + 2x, xey + cos x) (a) (4pts) Compute curl F. (b) (2pts) Is F conservative? Clearly indicate yes or no. (c) (8pts) Suppose C is the curve parameterized by r(t) = (t3 + 1, t– 2t) 0<t< 2 Compute ( F. dr.
2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and 2. Find the average value of the function f(x,y) y 2. (Sketch the region.) 1/, y xy over the region bounded by y x, and
Question Below are the graphs of f(x)= x²-3x²+1 and x² + y² = 2x²y2 a) Find the equation of the tangent line to the function (on left) at point (-1, f(-1)). 6) Calculate the slope of the tangent line to the function (on right) at point (1,1). 1- . 0,5 1 1.5 1 ST -1,8-1,694 -12 -1 -6.8-06-11-02 BIG 1 112 1,6 10