Limits: Use limit definition to find derivative of 1/2x + 5

[kmiller8054]

The directions are as follows: Use the limit definition to find the derivative of the function. I have no clue where to start at on this on.

f(x)=1/2x + 5

 

[pka]

Re: LIMITS

Which is it?
\(\displaystyle (1/2)x + 5\,,\,\frac{1}{{2x}} + 5,\,\mbox{ or } \,\frac{1}{{2x + 5}}\).
If you expect help, please learn the proper way to write the notation.

 

[stapel]

I have no clue where to start at on this on.

Um... Maybe one place "to start at on this on" would be to limit definition they gave you for the derivative...?

Note: Since different books use different definitions, you'll need to provide that definition when you reply showing your work so far. Also, you will need to clarify your meaning when you reply. As currently formatted, your function would appear to be "1/(2x) + 5", but you might mean "1/(2x + 5)", "(1/2)x + 5", or something else. :shock:

(It would be helpful if you either used the LaTeX formatting explained in the articles in the "Forum Help" pull-down menu at the very top of every forum page, or else used the formatting explained in the links in the "Read Before Posting" thread that you read before posting.)

Please be complete. Thank you!

Eliz.

 

[kmiller8054]

The problem is written the first way you have it written PKA. Thanks for any help.

 

[stapel]

Thanks for any help.

What formula did they give you? How far have you gotten in the plug-n-chug process?

Please be complete. Thank you!

Eliz.

 

[skeeter]

The directions are as follows: Use the limit definition to find the derivative of the function. I have no clue where to start at on this on.

f(x)=1/2x + 5

here's your clue ...

\(\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\)

 

[stapel]

here's your clue ...

\(\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\)

...if that's the formula the poster is supposed to use. There are others:

. . . . .\(\displaystyle \begin{array}{c}limit\\\Delta x\rightarrow 0\end{array}\, \frac{f(x\, +\, \Delta x)\, -\, f(x)}{\Delta x}\)

. . . . .\(\displaystyle \begin{array}{c}limit\\x\rightarrow a\end{array}\, \frac{f(x)\, -\, f(a)}{x\, -\, a}\)

. . . . .\(\displaystyle \begin{array}{c}limit\\\Delta x\rightarrow 0\end{array}\, \frac{\Delta f}{\Delta x}\)

...not to mention epsilon-delta proofs, and the original poster might not be able to move comfortably between these various options. :shock:

Eliz.

 

[pka]

Given the absolute simplicity of the function, I would bet that this is a epsilon-delta problem.

 

[galactus]

The poster said to find the derivative by the limit. I reckon it's safe to assume:

\(\displaystyle \lim_{h\to{0}}\frac{(\frac{x+h}{2}+5)-(\frac{x}{2}+5)}{h}\)

Simplify.