Evaluating Limits: {[ln (5 + h)]^2 - [ln 5]^2} / h as h->

[Lime]

Evaluate

lim
h-->0 {[ln (5 + h)]^2 - [ln 5]^2} / h

by recognizing it as a value of a certain derivative.

The concept of "limits" baffles me. I have no clue what the point of these types of questions are, nor do I know how to solve them. Please help.

 

[galactus]

Calculus is based on the concept of a limit. That's the point of the exercise.

\(\displaystyle \L\\\lim_{h\to\0}\frac{(ln(5+h))^{2}-(ln(5))^{2}}{h}\)

What's the derivative of \(\displaystyle (ln(x))^{2}\), evaluated at x=5?.

 

[Lime]

(1/x)^2 = (1/5)^2 = 1/25

What do I do with this then?

 

[pka]

Try \(\displaystyle \frac{{2\ln (x)}}{x}.\)

 

[galactus]

Check out this site on limits. It has a great tutorial on the formal definition using Macromedia Flash. Very nice.

http://archives.math.utk.edu/visual.cal ... index.html