Calculus 1

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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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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Trigonometric functions
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Exponential and logarithmic 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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Continuity
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Limit laws
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Equal or not?
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The limit laws
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The Squeeze Theorem
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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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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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Continuity and the Intermediate Value Theorem
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Roxy and Yuri like food
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Continuity of piecewise functions
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The Intermediate Value Theorem
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An application of limits
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Limits and velocity
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Instantaneous velocity
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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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Differentiability implies continuity
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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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The derivative of the natural exponential function
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The derivative of sine
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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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An unnoticed composition
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The chain rule
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Derivatives of trigonometric functions
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Higher order derivatives and graphs
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Rates of rates
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Higher order derivatives and graphs
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Concavity
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Position, velocity, and acceleration
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Implicit differentiation
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Standard form
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Implicit differentiation
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Derivatives of inverse exponential functions
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Logarithmic differentiation
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Multiplication to addition
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Logarithmic differentiation
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Derivatives of inverse functions
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We can figure it out
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Derivatives of inverse trigonometric functions
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The Inverse Function Theorem
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More than one rate
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A changing circle
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More than one rate
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Applied related rates
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Pizza and calculus, so cheesy
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Applied related rates
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Maximums and minimums
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More coffee
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Maximums and minimums
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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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Mean Value Theorem
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Let’s run to class
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The Extreme Value Theorem
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The Mean Value Theorem
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Linear approximation
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Replacing curves with lines
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Linear approximation
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Explanation of the product and chain rules
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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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L’Hopital’s rule
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A limitless dialogue
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L’Hopital’s rule
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Antiderivatives
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Jeopardy! Of calculus
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Basic antiderivatives
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Falling objects
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Approximating the area under a curve
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What is area?
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Introduction to sigma notation
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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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Antiderivatives and area
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Meaning of multiplication
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Relating velocity, displacement, antiderivatives and areas
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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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Applications of integrals
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What could it represent?
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Applications of 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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The Work-Energy Theorem
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Overall
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https://ximera.osu.edu/certificate/H4sIAAAAAAACA4WMuw7CMAxFf6XKTBvnQUKzMvADsCCWKPFQqW2kOJGQEP9OgtjxYuvec%2Fxiu9%2BQOXapSGW4EWZ2YLUvx57LhtlPieqEsfKeEjfG6%2BBFjAizMkYJQKX1DE2LvvRXEqQewY7SXgU4KZyw09Ge7o0IqWbqDN9SCnWtxINfv4dodVnK2tvzL3vsw79pSDcppNxMeH8AFhk8EdEAAAA%3D/GhzA34RUwOSntodf0p7yHDOsYjVszzxVreH2W7jyR3mpWdkyDh8wejbNb6NxorjAhw8nvo0b%2Bbho%2BnJQA7N1Z8T%2FdqEue3xm%2Bbzr7V2yGmGrcbIx9CF96oSMcXLud7Az%2FVuAGuFUjp6oBe10tANDIEnBxoUv4dQ3JRahEHgJwQm%2Bqt5Ki%2BHgRn5nL7PS2h1OtmJYSDSbfvSUUu2X1KySKwKW6gLGABCVyE%2BwrKWmNWlsIfxNKuY2A37y1%2Bbd2U7aCypzHD76Cmpc28QXJO8C2wQZ0uVpYVXKxc%2FuDK53HmTieKQWl%2Fi%2FP6lXwOhKntQqViY3Iwe51UaD6jeLJZ4RwA%3D%3D