A rectangular beam is to be cut from a cylindrical log of diameter 20 in. d in. d in. (a) Show that the cross-sectional area of the beam is modeled by the function A(0) = 200 sin 20 where 0 is as shown in the figure. A(0) = (20 cos 0)(20 sin 0) - 400 200 (b) Show that the maximum cross-sectional area of such a beam is 200 in2. [Hint: Use the fact that sin u achieves its maximum value at u = z/2.) A(0) = A( - 200 sin 2

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.