- 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
- 0.00%
- Applied related rates
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- Maximums and minimums
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- More coffee
- 0.00%
- Maximums and minimums
- 0.00%
- 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
- 0.00%
- 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
- 0.00%
- 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
- 0.00%
- Integrals are puzzles!
- 0.00%
- Working with substitution
- 0.00%
- The Work-Energy Theorem
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- Overall
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