Solving the Epsilon-Delta Problem with Sinusoidal Functions

[keemosabi]

Please Delete, Problem Solved

Please Delete, Problem Solved

 

[HallsofIvy]

What is the limit of sin(5x)/x as x goes to 0? Taking "A" as that value you want to find x such that |sin(x)/x- A|< 0.01.

 

[keemosabi]

The limit as sin(5x)/x goes to 0 is 5, right?

 

[Deveno]

as a practical matter you may want to find t such that:

|sin(t)/t - 1| < 0.01

then use x = t/5.

finding such a t (and thus x) isn't that hard (i did it by trial-and-error in about 2 minutes), the real trick is showing the inequality holds in the interval (-x,x). unless i am mistaken, the problem doesn't ask you to find the largest possible such x, just one that works.