## 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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