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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
Liner Regression The calculations for our sample size n = 10 are described below. The linear regression model is y = a + bx Table: Distance x miles
A train covered a certain distance at a uniform speed. If the train would have been 6km/hr faster, it would have taken 4hours less than the scheduled time. And if the train were
If arg (a/b) = pi/2, then find the value of ((a+b)/(a-b)) where a,b are complex numbers. Ans) Arg (a/b) =Pi/2 Tan-1 (a/b)= Pi/2 A/B = tanP/2 ,therefore a/b=infinity.
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Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
1) Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected". P(E) = 2) A s
how the parametric equations of parabola are derived?and what is the condition for the parabola whose equation is in the form of general equation of the two intersecting lines?
Properties of the Indefinite Integral 1. ∫ k f ( x ) dx = k ∫ f ( x ) dx where k refer for any number. Thus, we can factor multiplicative constants out of indefinite integral
Example determines the first four derivatives for following. y = cos x Solution: Again, let's just do so
Do you subtract when you add integers.
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