- #1

- 21

- 0

## Homework Statement

lim (4x^2+9) / (3x^2 +5) = 4/3

x->infinity

find k, such that x> k/sqrt(epsilon) guarantees abs((4x^2+9) / (3x^2 +5) - 4/3) < epsilon

## Homework Equations

## The Attempt at a Solution

By removing the absolute sign and making the denominator common, we get

7 / (9x^2 + 15) < epsilon

keep solving we get

x > 1/3 sqrt(7/epsilon - 15)

Here is where I got stuck. How do we find k as a constant? 15 is inside the square root and if we want to make the whole thing as a fraction we would get x > 1/3 sqrt((7-15*epsilon)/epsilon). I can't just get rid of 15 either because that would screw up the inequality and I am meant to find the MINIMUM value of k. Any help would be appreciated.