Given: limit of (sin x)/x as x --> 0 and that ε = .01 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.