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Problem 69

Estimating a Limit Consider the function $f(x)…

02:09
Problem 68

A sporting goods manufacturer designs a golf ball having a : volume of 2.48 cubic inches.
(a) What is the radius of the golf ball?
(b) The volume of the golf ball varies between 2.45 cubic inches. How does the radius vary?
(c) Use the $\varepsilon-\delta$ definition of limit to describe this situation. Identify $\varepsilon$ and $\delta .$

Answer

$\epsilon=\frac{0.843-0.836}{2}=0.0035$



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Video Transcript

Okay, Part A, we know sees two pi times the radius so plugging in. This gives us articles 1.2 sevens. The volume of the test ball is 4/3 pi times. The radius cubed equals 8.58 inches and coats volume. It's obviously cute. Okay, moving on into park be We know the amount of space taken up by the test ball is equivalent to the volume of a cylinder, which is subtracting the volume of three tennis balls. So we have pi times the radius 1.43 squared times the height minus three times the volume of the tennis ball, which we figured out in the previous slide. This gives us for 51.4 months, 25.7, which gives us 25.66 inches cute.

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