AB WS 041 Reimann Sum Approximation (2) 125% + Zoom Add Page Insert Table Chart Text Shape Media Comment 5 If a chart of values for f(x) - X -3 9 12 15 wa F(x) -1 O 0 If (1) dt Find a trapezoidal approximation of -3 using six subintervals of length At = 3 6 dy If 3x2 + 2xy + y? = 2, then the value of dx at x - 1 is 7 Ex for x If f(x) = (x2-1 for x > 1 then find 8 dV If V = ar , what is dr when r = 3? 9 If f(x) = x cos , then f' = Calc 1 Worksheet #41 Approximationg Areas using Reimann Sums 10 lim x' - 4x - x+4 x -4 x -4 11 The solution set of x + 8x + 23 is 12 x - - 4x Why does f(x) = x -2 on [0,4] not satisfy the hypotheses of Rolle's Theorem? 13 Find c for the Mean Value Theorem if f(x) - 2x- + 1 in [1,3]. 14 A function f that is continuous for all real numbers x has f(3) = - 1 and f(7) = 1. If f(x) = 0 for exactly one value of x, then which of the following could be x? A) - 1 B) 0 C) 1 D) 4 E) 9Zoom Add Page Insert Table Chart Text Shape Media Comment Cale 1 Worksheet #41 Approximationg Areas using Reimann Sums Approximate the area under - (x - ) on [0,4] using (a) 4 rectangles whose height is given using the left endpoint (b) 4 rectangles whose height is given using the right endpoint (c) 4 rectangles whose height is given using the midpoint (d) 4 trapezoids. (e) Evaluate the integral directly. Approximate the area under y - x2 1 on [0,4] using (a) 4 rectangles whose height is given using the left endpoint (b) 4 rectangles whose height is given using the right endpoint (c) 4 rectangles whose height is given using the midpoint (d) 4 trapezoids (e) (e) Evaluate the integral directly. Approximate to 3 decimal places the integral o with 4 equal intervals using: a) rectangles whose height is the right-hand endpoint b) rectangles whose height is the left-hand endpoint c) rectangles whose height is the midpoint of the interval d) trapezoids (trapezoidal rule) e) Evaluate the integral directly. Approximate the area under y - (x + 1) 2 on [ 0, 4] using (a) 4 rectangles whose height is given using the left endpoint, (b) 4 rectangles whose height is given using the right endpoint, (c) 4 rectangles whose height is given using the midpoint, and (d) 4 trapezoids. (e) Evaluate the integral directly. If a chart of values for f(x) X 12 15 F(x) -1 O 0 -1 15 Sf (t) dt Find a trapezoidal approximation of -3 using six subintervals of length At = 3 dy If 2 v2 + ? usr do $12= ? than tha value of dX at v = 1