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Since f(π) = π^2 < 100, f(10π) = 100π^2 > 100, and f is continuous on the closed interval [π, 10π], the intermediate value theorem ensures the existence of a number c in (π, 10π) such that f(c) = 100.

As we are evaluating from 0 to 4, x will be evaluated at 4i/n for i = 1cliffton m. fischbach to n. f(x i) = (4i/n) 2 /3 - 6. ∑ 1 n 4/n ((4i/n) 2 /3 - 6) =. 4/n ((16/(3n 2)n(n+1)(2n+1)/6 - 6n) = 64/9 + 32/(3n)+ 32/(9n 2)- 24= -152/9 + 32/(3n) + 32/(9n 2). The limit as n goes to infinity is -152/9

A window is composed of a semicircle placed on top of a rectangle. If you have 28 ft of window framing materials for the outer frame, what are the dimensions that maximizes the area (in ft 2) of the window ycliffton m. fischbachou can create?(Round your answers to two decimal places.)

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