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College Calculus |
Pre-Calculus |
Calculus for Engineering |
Differential Equations |
Financial Arithmetic |
Calculus for the Social Sciences |
Arithmetic
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Order of operations |
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Integers |
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Decimals |
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Fractions |
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Powers |
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Expanding brackets |
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Factoring |
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Algebra
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Calculating with fractions |
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Simplifying fractions |
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Fractions with variables |
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Binomial coefficients |
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Pascal's triangle |
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Factorials |
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Sigma notation |
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Applications of combinatorics |
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Applications of algebra |
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Formulas and graphs
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Substitutions |
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Formulas, tables and graphs |
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Linear equations
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Linear equations with a single unknown |
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Fractional linear equations |
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Equations with absolute values |
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Systems of linear equations |
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Linear equations of a line |
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Two linear equations with two unknowns |
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Quadratic equations
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ABC-formula |
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Completing the square |
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The quadratic equation |
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Factorization |
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Quadratic equations with one unknown |
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Intersection of two parabolas |
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Fractional equations |
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Root equations |
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Applications of quadratic equations |
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Linear inequalities
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Linear inequalities |
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Fractional linear inequalities |
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Linear inequalities with absolute values |
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One linear inequality with two unknowns |
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Multiple linear inequalities with two unknowns |
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Applications of linear inequalities |
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Exponential and logarithmic functions
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Rules of exponential functions |
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Equations with exponential functions |
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Logarithmic functions |
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Equations with logarithmic functions |
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Exponential growth |
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Translating functions |
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Scaling functions |
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Symmetry of functions |
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Composing functions |
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Applications of exponential and logarithmic functions |
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End value and constant value |
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Calculate interest and maturity |
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Equivalent percentages |
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Trigonometry
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Right-angled triangle |
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Degrees and radians |
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Differentiation
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Tangents to a curve |
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Derivatives of polynomials and power functions |
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Sum rule |
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Product rule |
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Quotient rule |
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Chain rule for differentiation |
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Derivatives of trigonometric functions |
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Quotient rule for differentiation |
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Derivatives of inverse functions |
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The natural logarithm |
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Derivatives of exponential and logarithmic functions |
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Approximation |
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Elasticity |
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Applications of differentiation |
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Set theory
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Sets |
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Operations of sets |
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Intervals |
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Functions
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Composition of functions |
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Operations for functions |
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Range of functions |
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Functions and graphs |
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Injective functions |
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Inverse of a function |
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Power functions |
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Equations and functions |
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Applications of function |
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Polynomials and rational functions
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Calculating with polynomials |
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Linear polynomials |
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Quadratic polynomials |
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Factorization of polynomials |
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GCD and LCM for of polynomials |
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Euclidean algorithm polynomials |
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Polynomial interpolation |
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Rational functions |
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Applications of polynomials and rational functions |
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Trigonometric functions
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Definitions of sin and cos |
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Right triangles and trigonometric functions |
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Periodicity and trigonometric functions |
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Calculating with trigonometric functions |
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Tangent and cotangent |
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Triangles and trigonometric functions |
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Inverse trigonometric functions |
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Limits
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Notion and rules of limits and infinity |
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Limits of rational functions |
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Horizontal & vertical asymptotes |
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Oblique asymptotes |
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Squeeze theorem for limits |
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Limits of exponential functions |
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Trigonometric limits |
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Applications of limits |
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Sequences and series
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The notion of sequence and series |
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Arithmetic series |
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The notion of sequence and series |
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Convergence & Divergence |
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Rules for limits of sequences |
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Power series |
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Length |
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Applications of sequences and series |
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Continuity
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Global minimum and maximum |
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Continuous extension |
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Min-max and intermediate value theorem |
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Limits of continuous functions |
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Rules for continuity |
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Applications of continuity |
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Analysis of functions
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Local minima and maxima |
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The mean value theorem |
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Monotonicity |
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Higher derivatives |
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Implicit derivatives |
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Linear approximation |
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Taylor series |
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The L'Hôpital rule |
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Applications of analysis of functions |
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Integration
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Antiderivation |
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Area |
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Riemann sums |
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Integral of a function |
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Calculation for integrals |
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Estimates of integrals |
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Mean value theorem for integrals |
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The fundamental theorem of calculus |
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Applications of integration |
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Multivariate functions
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Functions of two variables |
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Visualizing bivariate functions |
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Multivariate functions |
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Partial derivatives |
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Higher partial derivatives |
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Stationary points |
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Minimum, maximum, and saddle point |
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Criteria for extrema and saddle points |
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Convexity and concavity |
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Applications of multivariate functions |
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Applications of optimization |
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Introduction to Differential equations
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The notion of differential equations |
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Notations for ODEs |
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Order and degree of an ODE |
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Solutions of differential equations |
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Linear ODEs |
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Direction fields
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Direction fields |
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Euler's method |
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Autonomous ODEs |
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Existence and uniqueness of solutions of ODEs |
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Solution strategy on the basis of the slope field |
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Separation of variables
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Differentials |
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Differential forms and separated variables |
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Solving ODEs by separation of variables |
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Linear first-order differential equations
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Uniqueness of solutions of linear first-order ODEs |
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Linear linear first-order ODE and integrating factor |
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Solving linear first-order ODEs |
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Linear second-order differential equations
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Uniqueness of solutions of linear 2nd-order ODEs |
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Homogeneous linear 2nd-order ODEs with constant coefficients |
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Solving homogeneous linear ODEs with constant coefficients |
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The Ansatz |
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Solution methods for lineair second-order ODEs
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The Wronskian of two differentiable functions |
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Variation of constants |
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From one to two solutions |
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Solving linear second-order ODEs |
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Systems of differential equations
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Systems of couples linear first-order ODEs |
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Evaluating investments
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Accounting payback period |
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Average accounting return |
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Economic payback period |
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Net present value |
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Internal profitability |
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