A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must be 600 cm. In this problem you will find the base length a which will maximize the area of such a window. Use calculus to find an exact answer. When the base length is zero, the area of the window will be zero. There is also a limit on how large x can be: when a is large enough, the rectangular portion of the window shrinks down to zero height. What is the exact largest value of x when this occurs? largest a: cm. Determine a function A(x) which gives the area of the window in terms of the parameter x (this is the function plotted above): A(x) = cm2. Now find the exact base length x which maximizes this area: cm.

Q: х3-2х-1 lim x-3

A: This question is based on Limits

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Q: (а) lim х — 1

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Q: Find the following limits, clearly showing all of your work.

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Q: the limit cannot be zero for part b?

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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.