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Forgotten how to solve for square roots

  • Thread starter Dustobusto
  • Start date
1. The problem statement, all variables and given/known data

compute f'(x) using the limit definition.

f(x) = [itex]\sqrt{x}[/itex]

2. Relevant equations

f'(x) = [itex]\stackrel{lim}{h→0}[/itex] [itex]\frac{f(x+h)-f(x)}{h}[/itex]

3. The attempt at a solution

Plugging in the function values gives you

f'(x) = [itex]\stackrel{lim}{h→0}[/itex] [itex]\frac{\sqrt{(x+h)}-\sqrt{x}}{h}[/itex]

The end result is [itex]\frac{1}{2\sqrt{x}}[/itex] according to answer key.

I'm not sure how to go about solving. It's the square roots that are screwing me up. I have forgotten how to solve for square roots.

I've solved 6 problems within this context before coming across this one.
 
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1. The problem statement, all variables and given/known data

compute f'(x) using the limit definition.

f(x) = [itex]\sqrt{x}[/itex]

2. Relevant equations

f'(x) = [itex]\stackrel{lim}{h→0}[/itex] [itex]\frac{f(x+h)-f(x)}{h}[/itex]

3. The attempt at a solution

Plugging in the function values gives you

f'(x) = [itex]\stackrel{lim}{h→0}[/itex] [itex]\frac{\sqrt{(x+h)}-\sqrt{x}}{h}[/itex]

The end result is [itex]\frac{1}{2\sqrt{x}}[/itex] according to answer key.

I'm not sure how to go about solving. It's the square roots that are screwing me up. I have forgotten how to solve for square roots.

I've solved 6 problems within this context before coming across this one.
Try multiplying by the conjugate over itself. IOW, multiply by
$$ \frac{\sqrt{x + h} + \sqrt{x}}{\sqrt{x + h} + \sqrt{x}}$$
 
Understood. I got the answer now. Ty
 

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