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260 cheat sheets available

• Basics
• Laws of Exponents
  • Overview of the Laws of Exponents
  • First Law of Exponents (same base)
  • Second Law of Exponents (Same Exponents)
  • Law of Exponents: Radicals
  • Law of Exponents - Powers of Powers (multiple exponents)
• Equations and Inequalities
  • Solving Equations
  • Isolating the Square Root
  • Solving Inequalities
  • Absolute Value (In)Equations
  • Solving Absolute Value Equations with Roots
  • Inequalities with Nested Absolute Values
  • Solving Systems of Equations
  • Eliminating Variables
  • Addition Method
  • Gaussian Elimination
• Binomial Formula
  • The Binomial Formulas
  • Factorials
  • Pascal's Triangle
  • The Binomial Coefficient
  • The Binomial Theorem
• Fractions
  • Forming the Lowest Common Denominator
  • Expanding Fractions
  • Adding Fractions
  • Reducing Fractions
  • Compound Fractions
  • Factoring Terms
• Laws of Logarithms
  • Laws of Logarithms
  • First Law of Logarithms
  • The Second Law of Logarithms
  • Third Law of Logarithms
  • The Fourth Law of Logarithms
• Simplify terms
  • Factoring out
  • The Parentheses Gotta Go!
  • Compound Fractions
  • Reducing Fractions
  • Vertex Form
  • Completing the Square
  • Factoring Terms

• Calculus
• Proof by induction
  • Proof by Induction
  • Index Shifting
  • Extracting or adding members of a sum
  • Splitting up Sums
• Series
  • Convergence Tests for a Series
  • The Ratio Test
  • The Root Test
  • The Alternating Series Test
  • Comparison Test
  • Geometric Series
  • Partial Sums
  • Telescoping Series
  • Integral Test for Convergence
  • Important Series and their Limits
  • Absolute Convergence of a Series
  • The Harmonic Series
  • The General Harmonic Series
  • Power Series
  • Radius of Convergence of a Power Series
  • Taylor Series
  • Rates of Convergence
• Sequences
  • Sequences (of Real Numbers)
  • Limit of a Sequence
  • Zero Sequences
  • Limit Theorems
  • Limits of Sequences with a Fraction
  • Divergence
  • Sandwich Theorem for Sequences
  • Special Sequences and their Limits
  • Monotonicity of Sequences
  • Bounded Sequences/Functions
  • Arithmetic Progressions
  • Geometric Progressions
  • Alternating Sequences
  • Recursive Sequences
• Differentiation
  • How do I derive a function?
  • Deriving with the Constant Rule
  • Deriving with the Factor Rule
  • Deriving with the Power Rule
  • Deriving with the Sum Rule
  • Deriving with the Product Rule
  • Deriving with the Quotient Rule
  • Deriving with the Chain Rule
  • Logarithmic Differentiation
  • Differentiability (for functions with a single Variable)
  • The Fundamental Theorem of Calculus
  • The Differential
  • Absolute Error
  • Relative Error
  • Calculating Critical Points
  • Rolle's Theorem
  • The Mean Value Theorem
  • Extrema with Constraints
  • Calculating Inflection Points
  • L'Hospital's Rule
  • Tangent Line Approximations
  • Taylor Polynomials
  • Taylor Series
  • The Elasticity of Functions
• Sums and Products
  • Sums
  • Forming Generalized Formulas (for Sequences/Sums)
  • Pull a Factor out of a Sum
  • Index Shifting
  • Extracting or adding members of a sum
  • Splitting up Sums
  • Combining Sums
  • Important Sum Formulas
  • Calculation Rules for Products
• Integration
  • Important Integration Rules
  • Integrating Constants
  • The Power Rule in Integration
  • The Constant Factor Rule in Integration
  • The Sum Rule in Integration
  • Integration Tricks
  • Integration by Parts
  • Integration by Substitution
  • Important Integrals
  • Logarithm as Indefinite Integral
  • Indefinite Integrals
  • Definite Integrals
  • Finding Areas using Integration
  • Surface Area between Two Functions
  • Improper Integrals
  • Leibniz's Rule for Differentiation under the Integral Sign
  • Partial Fraction Decomposition
  • Polynomial Factorization
• Functions
• Applications
  • Intersection Points with Two Functions
  • Tangent Line Approximations
  • The Inverse Function
  • Completing the Square
  • Polynomial Factorization
  • Taylor Polynomials
  • Taylor Series
• Properties
• Domain and Range
  • Domain
  • Points of Discontinuity
  • Poles
  • Mathematical Singularities
  • Range
  • Bounded Sequences/Functions
  • Global Minimum/Maximum
• Draw Functions
  • Parameters of Functions
  • Table of Values for Functions
  • Symmetry of Functions
• Limits
  • Determining Limits
  • Limits of Sums
  • Taking the Limit of a Product
  • Limits of Sequences with a Fraction
  • L'Hospital's Rule
  • Limit of a Fraction
  • Limit Theorems
  • Divergence
• Continuity and Differentiability
  • Continuity of a Function (with a single variable)
  • Points of Discontinuity
  • Poles
  • Mathematical Singularities
  • Jump Discontinuities
  • The Intermediate Value Theorem
  • The Differential
  • Differentiability (for functions with a single Variable)
  • How do I derive a function?
• Roots, Critical- and Inflection Points
  • Methods for Calculating Roots
  • Calculating roots with the glqq pq formulagrqq
  • The Quadratic Formula
  • Distinction of Cases with Roots
  • Polynomial Long Division
  • Calculating Roots via Substitution
  • Calculating Roots with Newton's Method
  • The Intermediate Value Theorem
  • The Fundamental Theorem of Algebra
  • Calculating Critical Points
  • Global Minimum/Maximum
  • Calculating Inflection Points
  • How do I derive a function?
  • Monotonic Functions
• Types of Functions
  • Polynomial Functions
  • Linear Functions
  • The Absolute Value Function
  • Absolute Value (In)Equations
  • The Quadratic Function
  • Vertex Form
  • The Square Root Function
  • Rational Functions
  • The Exponential Function
  • The Exponential Function
  • The Logarithmic Function
  • Logarithm as Indefinite Integral
  • Trigonometric Functions
  • The Sine Function
  • The Cosine Function
  • The Tangent Function
  • Trigonometric Identities for Sums and Products of Sine/Cosine
  • Addition Theorems for Tangent
  • Specifying Degrees
  • Piecewise-defined Functions
  • Composite Functions

• Calculus II
• Multidimensional Functions
  • Domain of a Multidimensional Function
  • Partial Derivatives
  • The Gradient
  • Total Derivative
  • Directional Derivatives
  • The Hessian Matrix
  • Schwarz's Theorem
  • Laplace Operator
  • Del Operator
  • Divergence
  • Multidimensional Critical Points
  • Definiteness of a Matrix
  • Sylvester's Criterion
  • Testing for Definiteness with Eigenvalues
  • Multidimensional Critical Points with Constraints
  • Lagrange Multipliers
  • Lagrange: Determining the Type of Extremum via Bordered Matrix
  • Lagrange: Determining the Type of an Extremum via Hessian Matrix
  • Multidimensional Taylor Polynomials
  • The Tangent Plane
  • Implicit Functions
  • Level Curves
  • Global Extrema - Multidimensional Functions

• Linear Algebra
• Systems of Linear Equations
  • Systems of Linear Equations
  • Homogeneous Systems of Linear Equations
  • Nonhomogeneous Linear Systems
  • Solving a System of Linear Equations
  • Gaussian Elimination
  • Cramer's Rule
  • Matrix Equations
  • Kernel of a Matrix
  • Image of a Matrix
• Matrices
• Calculations of Matrices
  • Elementary Row Operations
  • Transposed Matrices
  • Matrix Addition
  • Scalar Multiplication of Matrices
  • Matrix Multiplication
  • Laws of Exponents for Matrices
  • Binomial Formulas for Matrices
  • Inverse of 2x2 Matrices
  • Gauss-Jordan Elimination
  • Inverting $n imes n$ Matrices
  • Calculating the Inverse with Adjugate Matrices
  • Matrix Equations
• Basics and special Matrices
  • Matrices
  • Transposed Matrices
  • Identity and Diagonal Matrices
  • Triangular Matrices
  • Elementary Row Operations
  • Gaussian Elimination
  • Gauss-Jordan Elimination
  • Row Echelon Form
  • Reduced Row Echelon Form
  • Triangular Form of Matrices
  • Inverse Matrix
  • Block Matrices
  • Multiplicaton of Block Matrices
  • Inverse of Block Matrices
• Determinants and Eigenvalues
  • Determinants
  • Determinants of $2 imes 2$ Matrices
  • Sarrus' Rule
  • Expanding Determinants
  • Calculation Rules for Determinants
  • Eigenvalues
  • Eigenspaces and Eigenvectors
  • Multiplicity
  • Definiteness of a Matrix
  • Testing for Definiteness with Eigenvalues
  • Minors
• Vector spaces
  • Vector Space
  • The Euclidean Space R^n
  • Linear Subspaces
  • Linear Span
  • Generating Sets
  • Basis
  • Dimension
  • Vectors
  • Linear Combination
  • Linear Dependence
  • Scalar Multiplication
  • Dot Product of Vectors
  • Vector Length
  • Normalize Vectors

• Geometry
  • The Pythagorean Theorem
  • Euclidean Distance
  • Equation of a Circle