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The Math

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Number Systems

This is where basic C.S. can be applied, compared to the number system.

Systems
  • N - Natural - 1, 2, 3, …
  • Z - Integers - -3, -2, -1, 0 , 1, …
  • Q - Rational - p/q where p and q are integers and q is not zero.
Special number systems

References

http://en.wikipedia.org/wiki/Number_system

Calculus 2

section 1

section 2

section 3

section 4

section 5

part 5.1

Examples part A

1.)ln((gz)/w) = (ln(g)+ln(z))-ln(w)
2.)ln(sqrt{a-17}) = 1/2ln(a-17)
3.)1/3(5ln(x+2)+ln(x)-ln(x^2-3)) = ln(root{3}{(x(x+2)^5)/(x^2-3)})
4.)lim{x right:2^+}{ln(x-2)} = -INFINITY
Find the derivative of the function for problems 5-11.
5.)f(x)=ln(2x) doubleright f prime(x)=1/x
6.)f(x)=8x^2ln(8x) doubleright f prime(x)=8x+16x*ln(8x)
7.)y=ln(xsqrt{x^2-1}) doubleright y prime =1/x+x/(x^2-1)
8.)f(x)=ln((6x)/(x+3)) doubleright f prime(x)=3/(x(x+3))
9.)y=ln(sqrt{(x+6)/(x-6)}) doubleright y prime=-6/(x^2-36)
10.)y=ln(root{6}{(x-3)/(x+3)}) doubleright y prime=1/(x^2-9)
11.)f(x)=ln(x+sqrt{4+x^2}) doubleright f prime(x)=1/sqrt{4+x^2}

Examples part B

Consider the following
1.)y=7x^2-ln(x), (1,7)
(a) Find an equation of the tangent line to the grap of f at the given point.
y=13x-6
(b) Use a graphing utility to graph the function and its tangent line at the point.

part 5.2

part 5.3

part 5.4

part 5.5

part 5.6

part 5.7

Test

plugin-exam1.pdf

section 6

part 6.1

part 6.2

Test

Exam 2

section 7

section 8

Test

plugin-exam3.pdf

section 9

part 9.1

part 9.2

part 9.3

part 9.4

part 9.5

part 9.6

part 9.7

Maclaurin Polynomial

Theorem
p_n(x)=f(0)+f'(0)x+f"(0)/2!+...+(f^n(0))/(n!)
Example 1.)

Taylor polynomial

Theorem
p_n(x)=f(c)+f'(c)(x-c)+f"(c)(x-c)^2/2!+...f^n(c)(x-c)^n/n!
Example 1.)

Test

plugin-exam4.pdf

section 10

Test

plugin-exam5.pdf

terminology & references

http://en.wikipedia.org/wiki/Cycloid
http://www.thefreedictionary.com/prolate ← Math terms
http://en.wikipedia.org/wiki/Focus_%28geometry%29
http://en.wikipedia.org/wiki/Vertex_%28geometry%29
http://en.wikipedia.org/wiki/Hypocycloid
http://en.wikipedia.org/wiki/Witch_of_Agnesi

section 11

section 12

Books & References

Calculus of a Single Variable by some a major douche
Math syntax used on this page
gnuplot
Calculus Super Review by Research & Education Association

user/afassett/start/math.txt · Last modified: 2011/06/02 14:15 by afassett