﻿ MATH 141 - PRECALCULUS

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MATH 141 – GOODIES FOR MIDTERM 2

(FALL 2023)

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FREE ONLINE GRAPHERS!

(Use shift-6 “^” for exponentiation.)

(Put restrictions in { }.)

(This has more with 3D graphing.  Try entering z = x^2 + y^2 and x^2 + y^2 + z^2 = 1)

2.4: i speaks

2.5:

Schoolhouse Rock! videos:

2.5: My Hero, Zero

2.5: A rendition by The Lemonheads! (same captions as above)

In memory of:

Bob Dorough (1923-2018)

2.6: Rational Graphs (HAs):

3.1: Inflation Calculator: https://www.usinflationcalculator.com

3.1: Coronavirus Cases

Deaths and Cases (CNN):

Vox on Asia (Omicron)

3.1: e

3.1: Dr. Evil (the "Austin Powers" series) too greedy:

Note: Actually, the GDP of the U.S. was a bit over \$1 trillion in 1969.

3.2: Log song:

3.2: Chemistry joke (pH - common logs): attached.

3.3: LOG LAWS

3.3: With great power … (don't abuse the Power Rule!)

• Observe that the population of India has been mostly increasing at an increasing rate; the graph is mostly concave up.  (The "second derivative" is positive.)  In other words, the rate of change (the first derivative) is increasing.

• Observe that the population of China has been mostly increasing at a decreasing rate; the graph is mostly concave down.  (The "second derivative" is negative.)  In other words, the rate of change (the first derivative) is decreasing.

• In both cases, the populations have been increasing; the first derivative of population with respect to time is positive in both cases.

3.4/3.5: NEWTON'S LAWS OF COOLING AND HEATING

FOR FUN

• "Family Guy" on y2k:

• Bill Maher on "Global Swarming" (Warning: Profanity):

• "MythBusters" on exploding water:

Zipf’s Law / Zipf’s Mystery (Math and reality!)

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