Forgotten how to solve for square roots

In summary, to compute f'(x) using the limit definition for f(x) = \sqrt{x}, you need to plug in the function values and use the formula f'(x) = \stackrel{lim}{h→0} \frac{f(x+h)-f(x)}{h}. This will result in \frac{1}{2\sqrt{x}} according to the answer key. To solve for square roots, you can try multiplying by the conjugate over itself.
  • #1
Dustobusto
32
0

Homework Statement



compute f'(x) using the limit definition.

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

Homework Equations



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

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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  • #2
Dustobusto said:

Homework Statement



compute f'(x) using the limit definition.

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

Homework Equations



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

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
$$ \frac{\sqrt{x + h} + \sqrt{x}}{\sqrt{x + h} + \sqrt{x}}$$
 
  • #3
Understood. I got the answer now. Ty
 

1. How do you solve for square roots?

To solve for a square root, you need to find the number that, when multiplied by itself, gives the original number. This number is called the square root.

2. What is the formula for solving square roots?

The formula for solving square roots is √x = y, where x is the number you want to find the square root of and y is the square root.

3. Can you explain the process of solving square roots?

To solve for a square root, you can use either the long division method or the prime factorization method. In the long division method, you divide the number into factors and find the square root of each factor. In the prime factorization method, you break down the number into its prime factors and take the square root of each factor.

4. Are there any tricks for solving square roots quickly?

One trick for solving square roots quickly is to memorize the squares of numbers from 1 to 10. This will help you recognize perfect squares and solve for them without having to use a calculator.

5. What are some common mistakes when solving square roots?

Some common mistakes when solving square roots include forgetting to simplify the square root, not using the correct formula, and forgetting to check for extraneous solutions. It is important to double check your work and make sure your final answer makes sense in the original equation.

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