Question

A positive number epsilon and the limit L of a function f at a is given. Find a number delta such that \[|f(x)-L|<\epsilon \] if 0<|x-a|2 4x-7=1; epsilon=.01

Answer 1

$$L=1,f(x)=4x-7,a=2,\epsilon=\frac1{100}$$correct?

Answer 2

$$|4x-7-1|<\frac1{100}\\|4x-8|<\frac1{100}\\4|x-2|<\frac1{100}\\|x-2|<\frac1{400}=\delta$$

Answer 3

Yeah, I get it now. Thanks for your help!

Answer 4

np @wesdg1978 we just solved for a bound on \(|x-2|\) somehow to pick for \(\delta\). In other problems it's not as direct!

Answer 5

Thanks, I've got a few more of these, so I may need some more help in a bit.