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Three Dimensional Spaces
In this section we will start taking a much more detailed look at 3-D space or R3). This is a major topic for mathematics as a good portion of Calculus III is completed in three (or higher) dimensional space.
We will be looking at the equations of graphs in 3-D (3 dimensional) space also vector valued functions and how we do calculus along with them. We will as well be taking a look at a couple of new coordinate systems for 3-D space.
This is the only section that exists in two places in my notes.
Here is a listing of topics in this section.
a. The 3-D Coordinate System
b. Equations of Lines
c. Equations of Planes
d. Quadric Surfaces
e. Functions of Several Variables
f. Vector Functions
g. Calculus with Vector Functions
h. Tangent, Normal and Binormal Vectors
i .Arc Length with Vector Functions
If the minute hand of a big clock is 1.05 m long, find the rate at which its tip is moving in cm per minute.
Area between Curves In this section we will be finding the area between two curves. There are in fact two cases that we are going to be looking at. In the first case we des
Arc Length with Polar Coordinates Here we need to move into the applications of integrals and how we do them in terms of polar coordinates. In this part we will look at the a
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Hypothesis Testing About The Difference Between Two Proportions Hypothesis testing about the difference between two proportions is used to test the difference between the propo
How do you simplify 10:30:45
Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:
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Definition 1. Given any x 1 & x 2 from an interval I with x 1 2 if f ( x 1 ) 2 ) then f ( x ) is increasing on I. 2. Given any x 1 & x 2 from an interval
Solve for x , y (x + y - 8)/2 =( x + 2 y - 14)/3 = (3 x + y - 12 )/ 11 (Ans: x=2, y=6) Ans : x+ y - 8/2 = x + 2y - 14 /3 = 3x+ y- 12/11
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