At Orange County Choppers, Paul Teutul Junior needs to make a circular metal dis

Question

At Orange County Choppers, Paul Teutul Junior needs to make a circular metal disk with area 1000 in^2. The radius of such a disk is squareroot (1000/pi) inches. To keep Paul Senior from blowing a gasket, Paul Junior must deviate from the ideal area of the disk, which is 1000 in^2, by less than plusminus 3 in^2. How close to the ideal radius must the Flowjet (the machine that cuts the disk) be to maintain tranquility at OCC? Answer = .02674 inches. In terms of the epsilon, delta definition of lim_x rightarrow a f (x) = L, let x be the actual radius of the disk and f (x) the actual area of the disk. What is the formula for the function f (x)? pix^2 What is the number a? squareroot (1000/pi) What is the number L? pi* (1000/pi) What value of epsilon is given? 3 What is the corresponding value of delta?

Explanation / Answer

Ans:

Let f be a function that is defined on an open interval containing "a" except possibly "a" itself, and let L be a real number. The statement

limxa f(x) = L

means that for every > 0 there exists a > 0 such that

if 0 < |x a| < then |f(x) L| <

Here

f(x) = pix^2

a = sqrt(1000/ pi)

L = 1000

= 3

=0.02674

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