i'm working on some problems at calc on the web.

The limit of x

^{2}as x approaches 2 is 4. That is,

lim

_{x -> 2}x

^{2}= 4

Let epsilon= 0.2.

Find delta > 0 such that

if | x - 2 | < delta

then

| x

^{2}- 4 | < 0.2

so far i've plugged f(x), L and epsilon into f(x)-L > epsilon to get:

x

^{2}-4 < 1/5, and i can see that it makes sense to go from there to

(x-2)(x+2)<1/5

so i need to get rid of the x+2 somehow to arrive at the same format as that for delta, but i have no idea how.

i'm having similar issues with this problem:

The limit of x

^{3}as x approaches 3 is 27. That is,

lim

_{x -> 3}x

^{3}= 27

Let epsilon = 0.2.

Find delta > 0 such that

if | x - 3 | < delta

then

| x

^{3}- 27 | < 0.2

i can see that x-3 is a factor of x

^{3}-27 but no idea on the cancelling