- #1

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Problem: Find the greatest c such that δ between zero and c is good. Give an approximation to three decimal places.

Equations:

0 < |x - a| < δ

0 < |f(x) - L| < ε

Attempt:

0 < |x - 0| < δ

0 < | sin(x)/x - 1| < ε

0 < | sin(x)/x - 1| < .01

0 < | sin(x)/x| < 1.01

0 < |sin(x)| < 1.01|x|

0 < |sin(x)| < 1.01δ

0 < |sin(x)|/1.01 < δ

Since sin(x) is going to range between -1 and 1, the greatest value for δ is 1/1.01. But, this answer isn't correct. The correct answer is .245, and I don't know how to get that.