Define f:[-1,∞]→ℝ as follows: f(0) = 1/2 and
f(x) =[(1 + x)^(1/2) - 1]/x , if x ≠ 0
Show that f is continuous at 0.
Definition. f is continuous at xo if xoan element of domain and
lf(x) - f(xo)l < ε whenever lx - xol < δ
The Attempt at a Solution
Do some algebra come up with f(x) = 1/[(1+x)^(1/2) + 1]
I also know that between [-1,1], f(x)≤ 1
and x ≥ 1, f(x) ≤ 1
I know I need to somehow pull out an lxl from the absolute value, since I know lxl≤δ then
I can define δ in terms of ε and the function.