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## Homework Statement

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.

## Homework Equations

Definition. f is continuous at x

_{o}if x

_{o}an element of domain and

lf(x) - f(x

_{o})l < ε whenever lx - x

_{o}l < 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.