Question

Consider the function below. lim x -> 3 (2x+1)=7

What values of x guarantee that f(x)=2x+1 is within 0.54 units of 7?

If x is within _____ units of 3, then f(x) is within 0.54 units of 7.

Answer 1

Let x=3±h where h is small, then f(3±h)=2(3±h)+1=7±2h, and this must equal 7±0.54.

So we remove 7 from each side, leaving 2h=±0.54, and h=±0.27.

If x is within 0.27 units of 3, then f(x) is within 0.54 units of 7.