# Precise definition for the limit

by realism877
Tags: definition, limit, precise
 P: 80 (4x+1)/(3x-4)=4.5 lim approaches 2 Find values of delta that correspond to epsilon=0.5 I know how to use the calculator to get the solution. I just want to know how to get rid of that nasty fractions to make things a lot easier.
Mentor
P: 20,409
 Quote by realism877 (4x+1)/(3x-4)=4.5 lim approaches 2 Find values of delta that correspond to epsilon=0.5 I know how to use the calculator to get the solution.
I'm not so sure. There's more to this than just plugging numbers into a calculator.

What you need to do is to find an interval around 2, (2 - δ, 2 + δ), so that no matter what x you pick in the aforementioned interval, (4x + 1)/(3x - 4) is between 4.5 - .5 and 4.5 + .5. IOW, between 4 and 5.
 Quote by realism877 I just want to know how to get rid of that nasty fractions to make things a lot easier.

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