CALCULUS
Formulas: Differentiation and Integration
Right Triangle and Pythagorean Theorem
Simplifying Rational Expressions
Partial Fraction Decomposition
Finding Limits Graphically and Numerically (Version 1)
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Finding Limits Graphically and Numerically (Version 2)
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Show graphically
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(ε-δ) Definition of Limit
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Continuity at a Point
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Intermediate Value Theorem
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Difference Quotient for Polynomial; Find f(x + Δx)
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Slope of Tangent Line at x = c (Version 1)
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Slope of Tangent Line at x = c (Version 2)
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Tangent Line (Writing Equation of )
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Draw Multiple Tangent Lines
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Derivative of f(x) at x (Version 1)
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Derivative of f(x) at x (Version 2)
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Derivative of f(x) at c (Version 1)
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Derivative of f(x) at c (Version 2)
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Derivative of Product and Quotient of Polynomial Functions
Implicit Differentiation (draw Graph of function and tangent line)
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Rolle's Theorem (new version)
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Rolle's Theorem (old version)
Mean Value Theorem (for derivative)
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The First Derivative Test
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(Also, Test for Increasing and Decreasing Functions)
The Second Derivative Test
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Newton's Method and Approximating Zero of Function (New Version)
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Newton's Method and Approximating Zero of Function
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Area Under Curve and Riemann Sum for y = f(x)
(Example: f(x) = x
2
+ 3x + 5 )
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Area Under Curve and Riemann Sum for x = g(y)
(Example: g(y) = y
3
- 5y + 5 )
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The Fundamental Theorem of Calculus
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Trapezoidal Rule for Definite Integral
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Simpson's Rule for Definite Integral
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Area Between Curves
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Solid of Revolution Revolving Around x-axis (or the line y = 0): Disk Method
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Solid of Revolution Revolving Around y =
c
: Washer Method
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Solid of Revolution Revolving Around y-axis (or the line x = 0): Disk Method
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Solid of Revolution Revolving Around x =
c
: Washer Method
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Solid of Revolution Revolving Around Vertical Line x =
c
: Shell Method
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Solid of Revolution Revolving Around Vertical Line x =
c
: Shell Method
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Solid of Revolution Revolving Around Horizontal Line y =
c
: Shell Method
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Solid of Revolution Revolving Around Horizontal Line y =
c
: Shell Method
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Arc Length
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Area of Surface of Revolution Revolving Around x-axis (or the line y = 0)
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Area of Surface of Revolution Revolving Around y-axis (or the line x = 0)
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Center of Mass of Planar Lamina With Uniform Density (ρ)
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Sequence and Series
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Finding limit of sequence {a
n
}
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Generating and Finding Limit of Sequence of Partial Sums {S
n
}
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Finding Sum of Series Σ
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n
th Term Test
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Geometric Series Test
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Telescoping Series
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Derivation of Parabola Equation
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Derivation of Ellipse Equation
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Derivation of Hyperbola Equation
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Area of Polar Region
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Derivation of Polar Equation of Parabola
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Derivation of Polar Equation of Ellipse
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Derivation of Polar Equation of Hyperbola
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Vectors
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Rectangular, Cylindrical, Spherical Systems
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Directional Derivative