## Lecture Notes: Wednesday, November 4, 1998

Ninth Homework
Assignment - for discussion at recitations on Tuesday November 10,
and Thursday November 12.

**Chapter 5 Review (Exam #4 is Tuesday, November 10)(Meyerson
Hall B1)**

exponential functions, rules.

e = limit(1+(1/n))^n as n -> infinity.

logarithmic functions, base

log[b](x) and b^x are inverse functions. Apply to e^x and
ln(x)

interest:

- simple
- compound
- continuous compounding

Present Value

Derivatives of e^x, ln(x). Also ln(|x|). Chain rule
computations.

logarithmic differentiation.

exponential growth and decay: **y = A*exp(k*t)**

Newton's law of cooling: **y = T + A*exp(-k*t)**

Logistic Curve: **y = P/(1+B*exp(-k*t))**

- Ex. 5.6 # 18. Growth of a population with environmental
limits.

Be sure to solve the Old Final Exam Problems from Assignment #8.
Also review MAPLE demonstrations #7, 8, 9, 10.

### Chapter 6 Section 1 (Antiderivatives and the Rules of
Integration)

F(x) anitderivative of f(x) means F'(x) = f(x).

Most general antiderivative of f(x) is F(x) + const

Indefinite Integral. Notation.

Antiderivatives of:

- constant
- x
- x^2
- x^n
- e^x
- 1/x
- f(x) +/- c*g(x)

Use of int and Int commands in MAPLE.

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