Calculus with Review - Full

Ximera tutorial
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How to use Ximera
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How is my work scored?
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Content for the First Exam
 
Equations and Inequalities
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Needed Score?
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Equations
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Inequalities
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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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What is a limit?
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Stars and functions
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What is a limit?
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Polynomial functions
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How crazy could it be?
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Working with polynomials
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End behavior
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Graphs of polynomial functions
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Rational functions
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Will it divide?
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Working with rational functions
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Rational equations and inequalities
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Graphs of rational functions
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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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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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Practice
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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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Slant 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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Practice
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Content for the Second Exam
 
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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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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Content for the Third Exam
 
Exponential and Logarithmic Functions
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An interesting situation
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Exponential and logarithmetic functions
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Derivatives of exponential functions
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Interesting changes
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The derivative of the natural exponential function
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Derivatives of exponential and logarithmetic 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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Trigonometric Functions
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Follow the bouncing pen.
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Trigonometric functions
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Derivatives of trigonometric functions
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How fast was the pen going?
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The derivative of sine
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Derivatives of trigonometric functions
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Maximums and minimums
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More coffee
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Maximums and minimums
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Additional content for Autumn Final Exam
 
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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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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Content for the First Exam
 
Review of Limits
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Guess the Value
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Review Limits.
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Review of differentiation
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Review Derivatives BreakGround
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Review 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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Explanation of the product and chain rules
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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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Implicit differentiation
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Standard form
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Implicit differentiation
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Finding dx dy
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Logarithmic differentiation
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Multiplication to addition
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Logarithmic differentiation
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Content for the Second Exam
 
Inverse Trigonometric Functions
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Inv Trig Function BreakGround
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Inverse trigonometric functions
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Derivatives of inverse trigonometric functions
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Derivatives of inverse trigonometric functions BreakGround
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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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L’Hopital’s rule
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A limitless dialogue
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L’Hopital’s rule
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L’Hopital’s rule for other forms
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Indeterminate mutterings
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L’Hopital’s rule for other forms
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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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Content for the Third Exam
 
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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Area approximations in sigma notation
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So many rectangles.
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Sigma Notation
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Area approximations with sigma notation
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Definite integrals
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Computing areas
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The definite integral
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Properties of the definite integral
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Computing areas
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Properties of 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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Applications of integrals
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What could it represent?
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Applications of integrals
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Additional content for the Final Exam
 
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/H4sIAAAAAAACA4WMywrCMBQFfyVkbds8msZmK%2BheFEHchCRiIG0hDyuI%2F26ixa13c2GYOU84ysFAAXfJhAiOwXi4gqk8AR92MF7WU0i10akpNDQdZ%2FhKOoQ4otrQK%2B57wpBuc6ZlLFMEkbbCpELsgNeCMoFJzTk9Z0NNyYfiNEo6lVwKs403b%2B7WzD90ymj%2FQdvkXK6ija5Em0UAJQJfBVSXEfy7rCxTQU0%2BT6HXG6s%2BX9r5AAAA/WJjG11ERM%2BJqWLULqSSPyCiMlYrVExhR%2Fz%2BVe8Yqezy6wfJ7cBmG4va%2BfGDa4ZmiMKF1ztwbBdSCRslhJKI%2FmcOKBPl%2BOTVBI9eqEfY4FDtjUXhCdV9SdbZzsHxC%2Fs0LGs2w%2FAE4LqxZ9sAHeWGqUoac8PkxkOeOHXpyFsNggGo2N%2F6oAcNXF%2BUrffNgQDtS34d6AKHRK%2BnejSiTvLv7e1CMqka%2BwsHHy7Kxn%2B4IGN2CLCjj33r%2F4L8wl15N28ujbURHnFfg%2BFxy0WFhsShEm%2FFKU36Gk9Nb1u4ZU439UhEptRa00ZOdm9EmrvQuEngg%2B3H0Rr8AXd3WoX%2FMcP21Bw%3D%3D