DELTA-EPSILONS

1) What is the limit of f(x) = 3x^{2}- 2x - 4 as x approaches 2?

Obviously it is 4, now to 1a)

1a) For epsilon = 0.01, find a value of delta so that f(x) is closer to the limit than epsilon. Apply the same for when epsilon = 0.001.

2) What is the limit of f(x) = sqrt(x) as x approaches 9?

Obviously it is 3, now to 2a)

2a) For epsilon = 0.01, find a value of delta so that f(x) is closer to the limit than epsilon. Apply the same for when epsilon = 0.001.

Now, I actually started both #1 and #2. My work, respectively:

1a) Let epsilon = 0.01

- |f(x) - L| < epsilon
- |3x^2 - 2x - 4 - 4| < 0.01
- -0.01 < 3x^2 - 2x - 8 < 0.01

Now, where do I go from here?

2a) Let epsilon = 0.01

- |f(x) - L| < epsilon
- |sqrt(x) - 3| < 0.01
- -0.01 < sqrt(x) - 3 < 0.01
- 2.99 < sqrt(x) < 3.01
- 2.99
^{2}< sqrt(x) < 3.01^{2}- 8.9401 < x < 9.0601

Now, where do I go from here?