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Optimal Polynomial Approximation (theoretically general version)
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Expression 3: "f" left parenthesis, "x" , right parenthesis equals sine left parenthesis, "x" , right parenthesis
f
x
=
s
i
n
x
3
Orthonormal Basis
Orthonormal Basis
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4
Optimal dth Degree Polynomial
Optimal dth Degree Polynomial
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9
Variable Setup
Variable Setup
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12
23
powered by
powered by
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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Examples
Lines: Slope Intercept Form
example
Lines: Point Slope Form
example
Lines: Two Point Form
example
Parabolas: Standard Form
example
Parabolas: Vertex Form
example
Parabolas: Standard Form + Tangent
example
Trigonometry: Period and Amplitude
example
Trigonometry: Phase
example
Trigonometry: Wave Interference
example
Trigonometry: Unit Circle
example
Conic Sections: Circle
example
Conic Sections: Parabola and Focus
example
Conic Sections: Ellipse with Foci
example
Conic Sections: Hyperbola
example
Polar: Rose
example
Polar: Logarithmic Spiral
example
Polar: Limacon
example
Polar: Conic Sections
example
Parametric: Introduction
example
Parametric: Cycloid
example
Transformations: Translating a Function
example
Transformations: Scaling a Function
example
Transformations: Inverse of a Function
example
Statistics: Linear Regression
example
Statistics: Anscombe's Quartet
example
Statistics: 4th Order Polynomial
example
Lists: Family of sin Curves
example
Lists: Curve Stitching
example
Lists: Plotting a List of Points
example
Calculus: Derivatives
example
Calculus: Secant Line
example
Calculus: Tangent Line
example
Calculus: Taylor Expansion of sin(x)
example
Calculus: Integrals
example
Calculus: Integral with adjustable bounds
example
Calculus: Fundamental Theorem of Calculus
example
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