# Finding the Limit by Interpreting an Expression as an Appropriate Derivative

1. Nov 19, 2009

### Loppyfoot

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

Find Lim [ 1/h*ln(3+h)/(3)] by interpreting the expression as an appropriate derivative.
h→0

2. Relevant equations

I am confused on how to solve this problem for a review packet for Calc BC. I seem to have forgotten how to solve this problem and hopefully someone can give me some pointers!

2. Nov 19, 2009

### Staff: Mentor

Are you sure you have the problem written correctly? Something like this, maybe?
$$\lim_{h \rightarrow 0}\frac{ln(3 + h) - ln(3)}{h}$$

What you have doesn't look like a limit expression for any derivative that I can think of.

3. Nov 20, 2009

### HallsofIvy

Staff Emeritus
The second "3" should be inside the logarithm: ln((3+h)/3)= ln(3+h)- ln(3)

(1/h) ln((3+h)/3)= (1/h)(ln(3+h)- ln(3)) is the difference quotient for the derivative of ln(x) at x= 3.

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