Basic Differentiation
Subject:
The derivative is the instantaneous rate of change of a given function.
FORUMLA:
lim as h approaches 0 of f(x+h)- f(x)/h
Calculus
Forum reference:
Book page:
http://course-notes.org/Calculus
Precalculus! Chapter 1.1
Subject:
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Calculus Workbook
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Definition and Domain of Rational Functions
Subject:
Definition and Domain of Rational Functions
A rational function is defined as the quotient of two polynomial functions.
f(x) = P(x) / Q(x)
Here are some examples of rational functions:
g(x) = (x2 + 1) / (x - 1)
h(x) = (2x + 1) / (x + 3)
The rational functions to explored in this tutorial are of the form
f(x) = (ax+b)/(cx + d)
where a, b, c and d are parameters that may be changed, using sliders, to understand their effects on the properties of the graphs of rational functions defined above.
Example: Find the domain of each function given below.
g(x) = (x - 1) / (x - 2)
h(x) = (x + 2) / x
Solution
Life science Problems
Subject:
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AP CAL WEB
Subject:
http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/
Nice website for calculus
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Functions
Subject:
If it passes the vertical line test, it is a function.
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Derivative
Subject:
Instead of doing the limit process of finding a derivative, there is a much more effective method of finding a derivative.
X^N -> the derivative would be -> N(X)^N-1
Say for example, you have f(x) = x^2, it would be 2(x)^(2-1), which would be 2x^1, or just 2x.
if you have 3x^3, it would be 3(3)x^(3-1), which would be 9x^2
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Math Formulae List
Subject:
SAT Subject Math Level 2 Facts & Formulas Numbers, Sequences, Factors Integers: . . . , -3, -2, -1, 0, 1, 2, 3, . . . Reals: integers plus fractions, decimals, and irrationals ( ? 2, ? 3, pi, etc.) Order Of Operations: PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract) Arithmetic Sequences: each term is equal to the previous term plus d Sequence: t1, t1 + d, t1 + 2d, . . . The nth term is tn = t1 + (n? 1)d Number of integers from in to im = im ? in + 1 Sum of n terms Sn = (n/2) ? (t1 + tn) Geometric Sequences: each term is equal to the previous term times r Sequence: t1, t1 ? r, t1 ? r2, . . . The nth term is tn = t1 ? rn?1 Sum of n terms Sn = t1 ? (rn ? 1)/(r ? 1) Sum of infinite sequence (r < 1) is S? = t1/(1? r)
Limits to infinity
Subject:
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If a limit is approaching infinity, the highest exponent on the numerator or denominator determines whether its zero, or infinity
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Pages
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