# Proving Operating Functions

1. May 6, 2009

### banana_banana

1. The problem statement, all variables and given/known data

If P(x)=x^(1/2)
show that P(x+h)-P(x)=h/[(x+h)^(1/2)+ x^(1/2)]

2. Relevant equations

3. The attempt at a solution

pls help me. I don't have any idea of this...

2. May 6, 2009

### Cyosis

Try multiplying by:

$$\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}$$

3. May 6, 2009

### banana_banana

Will i going to substitute it on the x variable? I don't know where it needs to be multiplied.

4. May 6, 2009

### HallsofIvy

Staff Emeritus
"Multiply" doesn't mean substitute!

First form P(x+h) by replacing x with x+ h. Then subtract P(x) from that. That's what "P(x+h)- P(x)" means! Cyanosis is suggesting that you can get the final form you want by multiplying by
$$\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}$$

5. May 7, 2009

### banana_banana

tnx for the explanation. :)