Chapter 7
Section 2
Natural
Logarithmic Function
x > 0
ln x is the area under the
hyperbola y
= 1 from t
= 1 to t = x for x = 1
For 0 < x < 1
Part
1 of the Fundamental Theorem of Calculus:
so… 
*use
these in order to expand
logarithmic equations and expressing the equation as a single logarithm.
Laws of Logarithms:
Example #1
Expanding Logarithmic Equations:
Example
#2
Expressing
Logarithmic Equations Logarithm:
IMPORTANT
FACT:
In
order to graph y = ln(x)
AND
AND
In
order to differentiate ln(u)
you must use the chain rule.
*Remember,
the chain rule
differentiates with respect to u and then multiplies by the derivative
of u
with respect to x.
Example: 
Some
Links they may HELP you:
For Fundamental Thereom of Calculus:
http://archives.math.utk.edu/visual.calculus/4/ftc.9/
http://www.ies.co.jp/math/java/calc/perime/perime.html
http://www.math.hmc.edu/calculus/tutorials/fundamental_thm/