Proof of Square Root Limit Theorem for Continuous Functions

[dopey9]

square root limit proof

R is the real nmbers

so let A be in R
let f: A -> R be such that f(x)>0 for all x in A
c is in A

Does anyone know the proof to or even get me started on this proof shown below

[It's hard to write roots on the computer, so I will use the 1/2-th power instead.] SO i want to prove the following

lim x ->c [f(x)^(1/2)] = [lim x->c f(x)]^(1/2), PROVIDED f(x) > 0

 

[AiRAVATA]

Use the continuity of the square root and the definition of limit.

 

[HallsofIvy]

In other words, this function, f, has very little to do with the question. The definition of "h(x) is continuous at x=a" is lim(x->a) f(x)= f(a). In this case, what is a?