Thread: Prove continuity at a point using epsilon/delta

Hi,
I need to prove that f(x) = cuberoot[x+3] is continuous at x = -2 (using: u^3 - v^3 = (u-v)(u^2 + uv + v^2). I know that I need to manipulate mod(f(x) - f(-2)) to be less than epsilon for some delta but I'm struggling with the algebra.
Any help would be greatly appreciated!

Originally Posted by s0791264

Hi,
I need to prove that f(x) = cuberoot[x+3] is continuous at x = -2 (using: u^3 - v^3 = (u-v)(u^2 + uv + v^2). I know that I need to manipulate mod(f(x) - f(-2)) to be less than epsilon for some delta but I'm struggling with the algebra.
Any help would be greatly appreciated!

at x = -2

what you want to show is the following:

for , there exists such that:

for all x that belongs to dom f\{c} s.t.

i remember working backward in problem like these. Start out with something like this...

let ,

for



... (you'll prolly need to use some algebraic formula for cube/cluberoots and perhaps triangle inequality as well
...
...




P.S. I'll try this later on.