Tangent line Archives - The Nature of Mathematics - 13th Edition

Reference Topics 18-3

May 21, 2024July 23, 2015 by elaine

This is a more advanced site than we need for the introduction in this book, but check out the following choices on this site:
“Secants and tangents”
https://www.mathsisfun.com/geometry/tangent-secant-lines.html… See the whole entry

Homework Hints 18-3

May 20, 2024July 23, 2015 by elaine

Problems 1-4
Follow the steps in Example 1 for the distances given in Table 18.1.

Problems 5-8
These problems are designed to develop your sense of what is meant by average rate of change. See Example 3.

Problems 9-12
These … See the whole entry

Section 18.3: Derivatives

September 27, 2015July 23, 2015 by elaine

18.3 Outline

Average rate of change
Instantaneous rate of change
Derivative
1. derivative of f at x
2. differentiable function
3. derivative of e^x
Tangent line
1. tangent-line
  formula
2. equation of tangent line at a point (h, k ).
Velocity

18.3

… See the whole entry

Section 18.1: What is Calculus?

September 28, 2015July 23, 2015 by elaine

18.1 Outline

What is Calculus?
1. Calculus is the mathematics of motion and change.
2. The three main ideas of calculus are limit, derivative, and integral
The Limit: Zeno’s Paradox
1. Achilles and the tortoise
2. limit of a sequence
The derivative: the tangent

… See the whole entry