Precise definition for the limit

[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 just want to know how to get rid of that nasty fractions to make things a lot easier.

 

[Mark44]

(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.

I just want to know how to get rid of that nasty fractions to make things a lot easier.