Business Calculus

Ximera tutorial
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How to use Ximera
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How is my work scored?
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Understanding functions
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Same or different?
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For each input, exactly one output
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Compositions of functions
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Inverses of functions
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Increasing and Decreasing Nature of Functions
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Financial Mathematics
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Review of famous functions
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How crazy could it be?
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Polynomial functions
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Rational functions
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Exponential and logarithmetic functions
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What is a limit?
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Stars and functions
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What is a limit?
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Limit laws
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Equal or not?
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Continuity
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The limit laws
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Continuity of piecewise functions
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(In)determinate forms
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Could it be anything?
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Limits of the form zero over zero
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Limits of the form nonzero over zero
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Continuity and Intervals
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Why does it work?
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The Intermediate Value Theorem
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Sign Tables
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Solving Inequalities
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Definition of the derivative
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Slope of a curve
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The definition of the derivative
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Derivatives as functions
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Wait for the right moment
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The derivative as a function
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3
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Rules of differentiation
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Patterns in derivatives
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Basic rules of differentiation
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Product rule and quotient rule
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Derivatives of products are tricky
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The Product rule and quotient rule
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Chain rule
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A coincidence?
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The chain rule
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Derivatives of Exponential Functions
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Exponential Functions and Derivatives
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The derivative of the natural exponential function
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Derivatives of general exponential functions
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Derivative of Logarithmic Functions
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We can figure it out
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Derivatives of inverse exponential functions
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The Inverse Function Theorem
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Implicit differentiation
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Standard form
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Implicit differentiation
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Logarithmic differentiation
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Multiplication to addition
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Logarithmic differentiation
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Higher order derivatives
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Higher order derivatives
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Linear approximation
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Replacing curves with lines
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Linear approximation
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Maximums and minimums
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More coffee
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Increasing and Decreasing
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Maximums and minimums
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Concavity and the Second Derivative Test
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Rates of rates
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Concavity
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Second derivative test
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Global Extrema on Closed Intervals
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The Extreme Value Theorem
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Finding Extrema on Closed Intervals
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Using limits to detect asymptotes
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Zoom out
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Vertical asymptotes
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Horizontal asymptotes
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Concepts of graphing functions
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What’s the graph look like?
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Concepts of graphing functions
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Computations for graphing functions
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Wanted: graphing procedure
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Computations for graphing functions
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Optimization
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A mysterious formula
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Basic optimization
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Applied optimization
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Volumes of aluminum cans
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Applied optimization
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Antiderivatives
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Jeopardy! Of calculus
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Basic antiderivatives
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Integration with Initial Conditions
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Integration With Initial Conditions
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Approximating the area under a curve
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What is area?
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Approximating area with rectangles
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Definite integrals
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Computing areas
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The definite integral
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First Fundamental Theorem of Calculus
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What’s in a calculus problem?
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The First Fundamental Theorem of Calculus
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Second Fundamental Theorem of Calculus
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A secret of the definite integral
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The Second Fundamental Theorem of Calculus
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A tale of three integrals
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The idea of substitution
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Geometry and substitution
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The idea of substitution
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Working with substitution
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Integrals are puzzles!
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Working with substitution
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Areas between curves
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Area between curves
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Consumers’ and Producers’ Surplus
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Consumers’ and producers’ surplus
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Introduction to differential equations
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Modeling the spread of infectious diseases
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Differential equations
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Separable differential equations
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Functions of several variables
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Functions of several variables
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Partial derivatives
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Partial derivatives
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Overall
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https://ximera.osu.edu/certificate/H4sIAAAAAAACA4WMwQqDMAyGX0V6nppqtdrjdtgLbJexS9UIQlVoGhiMvftaGGO35fKH5Pu%2Fp9jsisKIMyOF7EroxUFwCiMey4reFjtxgROX6Uplq1Wjh6YDDfWE9Sz7HubOqlibbEiqCiqVS5lX7QW0UWCgK6SUt0iMO3tKTDkwLRsSfZeTdSM7pkiFJbgEHT%2Bv%2B5b9m4j8CGjcfRTA6w0%2FcxgC3wAAAA%3D%3D/wP8hdiY2Vm6vNdVfuedGCD0C8QrS%2FpfjvIrrkJEMLugKejXFHHHglWR3KmQ4mT1%2FCq9tllaSSQo98W%2BSfd0eHbEgp6fyMlZLdU6JzFccZBghF6%2B%2FzTEjKbSaD0gZ7h8p0yt9QWEvmYQrRBVjBR8IfanejlOI20yVCHAurPch4gLu5mD%2FNAbYQKBU%2ByIXQ8S3Yhiq6q1rF4HWUav8Tt%2Bs4k8BxYzmmK5iDyNymG28iOJwnB%2BxyYMTDCErTxySbyvkQSrXAD4ZwoMQ9SMUxjHexMcBIpHRyPipsgvAuyVgrBOZm54Nuk%2Bz%2F25398TtD%2FNrF8aQUcFpbVkKdIsPJ1CZaQ%3D%3D