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|

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|<delta. 

lim x-->2 4x-7=1; epsilon=.01

anonymous · Answer

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

anonymous · Answer

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

wesdg1978 · Answer

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

anonymous · Answer

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

wesdg1978 · Answer

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