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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
Ratio - situations in which we need to compare two quantities in terms of their ratio. (e.g., if Munna weighs 40 Kg. and Munni weighs 50 Kg., find the ratio of their weights.)
SOLVE THE inequation 0>-5 -X AND X Belongs TO R .Represent THE SOLUTION SET ON THE NUMBER LINE
We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2
write CxD being sure to use appropriate brackets and find n(CxD)
Tabulated values of the dynamic and kinematic viscosity of aqueous sodium chloride solutions have been researched in the academic literature (Kestin et al 1981). The data availab
Here we look at only the rules without going into their proofs. They are: a 0. If a If a If a
what is the importance of solid mensuration?
Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example Graph y = - 2/5 x + 3 .
Explain How to Distribute simplifying expressions? The distributive law states that for all numbers a, b, and c, a(b + c)= ab + ac What does this mean in plain language?
mr ouma bought two sets of spanners for sh 300per set two machanic vice at sh 1000each three set of screw driver at sh 115 per set and tool box for sh 300
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