Let An be the area of a polygon with n equal sides inscribed in a circle with ra

Question

Let An be the area of a polygon with n equal sides inscribed in a circle with radius gamma . By dividing the polygon into n congruent triangles with central angle 2 pi /n, determine which of the following is a correct expression for An : 1/2nr2sin(pi /n) 1/2n2rsin (2 pi /n) nr2sin (2 pi /n) nr2sin (2 pi /n) Compute the limit as n goes to infinity of the correct answer to (a). Value of limit = (a) Estimate the area under the graph of f (x) = 7 + X2 from X = - 1 to X = 2 using three approximating rectangles and right endpoints. R3 = Repeat part (a) using six approximating rectangles and right endpoints. R6 = Repeat part (a) using three approximating rectangles and left endpoints. L3 = Repeat part (a) using six approximating rectangles and left endpoints. L6 = Repeat part (a) using three approximating rectangles and midpoints. M3 = Repeat part (a) using six approximating rectangles and midpoints. M6 = Based on sketches of the graph of f(x) and the approximating rectangles, which appears to be the best estimate? L3 R6 M6 M3 R3 L6 Estimate the area under the graph of f (x) = 25 - X2 from X = 0 to X = 5 using five approximating rectangles and right endpoints. R5 = Repeat part (a) using left endpoints. L5 = By looking at a sketch of the graph and the rectangles, determine for each estimate whether it overestimates, underestimates, or is the exact area. L5 R5

Explanation / Answer

a. C b. pi r^2 c.

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