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MATH 140 WIR3 #17
Answering questions about a demand and supply word problem
Answering questions about a demand and supply word problem
Discussing properties of linear functions
Writing the equation of a line that passes through two points
Writing the equation of a line with an undefined slope and a given point
Writing the equation of a line with a zero slope given a point
Finding a linear demand equation
Writing a linear function representing the depreciation of a car
Finding the equation of a line through two points
Finding the equation of a line through two points
Finding the equations of parallel and perpendicular lines
Finding the equation of a parallel line
Discussing how to write the equation of a line through two given points
Writing a linear equation of profit from a business word problem
Graphing a line without using technology
Graphing a line without using technology
Determining the change in y as x increases for a line
Determining the change in x as y decreases for a line
Writing a function for the value of an item depreciating linearly over time
Finding linear functions for the cost, revenue, and profit of a business
Finding the linear cost function for a company
Finding the linear revenue function for a company
Finding a linear supply function
Finding the solution to a system of linear equations by graphing
Graphing the solution set of an inequality with two variables
Graphing the solution set of an inequality with two variables
Graphing the solution set of system of linear inequalities
Finding the piecewise-defined function for a given graph along with its domain and range
Writing a non-linear function to represent the line graphed on a semilog plot
Finding a tangent line to an curve defined implicitly
Finding a tangent line to an curve defined implicitly
Finding the equation of a tangent line to a function containing a logarithm
Finding the tangent line to a parametric curve
Finding the tangent line to a parametric curve
Finding the equation of a tangent line to a parametric curve
Finding the equation of a tangent line to an implicit function
Finding the tangent line to a parametric curve
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Finding the slope of a line through a pair of points
Finding the x and y-intercepts for a line
Determining the slope of a line given points containing a variable
Finding the change in y as x increases for a given line
Writing a non-linear function for the graph containing two points on a double-log plot
Explaining the definition of logarithmic scale and double-log plots
Explaining the logarithmic scale and a semilog plot
Cartesian equations and parametric equations of curves
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Review of the limit definition of a derivative and calculating the derivative
Derivatives and tangents to curves
Finding the distance between a point and a line using scalar projection
Finding the point when the tangent line to a function has a particular slope
Cartesian equations and parametric equations of curves
Using the limit definition to find derivatives of functions and vector functions
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Using the limit definition to find derivatives of functions and vector functions
Using the limit definition to find derivatives of functions and vector functions
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Using Python to find the equation of the tangent line to a curve and graphing the result
Solving a linear equation algebraically and showing how this relates to the graph
Solving a linear equation algebraically
Solving a linear equation algebraically and showing how this relates to the graph
Explaining the format and possible solutions for a system of two linear equations
Solving a system of linear equations with two variables
Solving a system of two linear equations with two variables using the elimination method
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Explaining the format and possible solutions for a system of two linear equations
Solving for a constant so a line has a particular x-intercept
Graphing a line without using technology
Finding the linear profit function for a company
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Determining the end behavior, real zeros, domain, and y-intercept for a polynomial
Graphing a piecewise function
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
Finding the properties of an exponential function including domain, range, end behavior, and intercepts
Finding the domain, intercepts, asymptotes, and holes of a rational function
Finding the domain, intercepts, asymptotes, and holes of a rational function
Finding the domain, intercepts, asymptotes, and holes of a rational function
Using logarithms to transform a power function into a linear function
Determining the properties of a rational function and graphing it
Determining the properties of a rational function and graphing it
Determining properties of an exponential function
Determining properties of an exponential function
Determining properties of an exponential function
Identifying the graph of an exponential function
Determining properties of an exponential function
Determining the properties of a logarithmic function
Determining the graph of a logarithmic function
Determining the properties of a logarithmic function
Determining the graph of a logarithmic function
Tangent lines to parametric equations and related rates examples
Review of vector functions and parametric equations
Review of limits and derivatives of inverse trigonometric functions
Implicit differentiation and physics applications of derivatives
Derivatives of parametric equations and tangent lines
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Review of limits and derivatives of inverse trigonometric functions
Limits at infinity and asymptotes, along with physics applications
Limits at infinity, asymptotes, and tangent lines
Derivatives of exponential and logarithmic functions and the exponential model
Derivatives of exponential and logarithmic functions and the exponential model
Tangent lines to parametric equations and related rates examples
Finding a vector equation for the line through two points
Finding a parallel vector through a point
Finding a line perpendicular to a vector and passing through a point
Find the Cartesian form and sketch the graph for the parametric equation of a line
Finding the points on a parametric curve where the tangent line is horizontal or vertical
Finding the linear approximation for a function
Finding where a function has horizontal tangent lines
Using a linear approximation to approximate the value of a function
Finding where the tangent line is horizontal or vertical for a parametric equation
Using the first and second derivatives to sketch the graph of a function
Finding a vector equation for the line passing through two points
Finding when the tangent line to a parametric curve is vertical or horizontal
Examples finding a volume using disks, washers, and by slicing
Tangent lines to parametric equations and related rates examples
Review of vector functions and parametric equations
Review of limits and derivatives of inverse trigonometric functions
Implicit differentiation and physics applications of derivatives
Derivatives of parametric equations and tangent lines
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Review of limits and derivatives of inverse trigonometric functions
Proving limits using the epsilon-delta definition
Limits at infinity and asymptotes, along with physics applications
Limits at infinity, asymptotes, and tangent lines
Proving facts about differentials including a product rule
Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine
Derivatives of exponential and logarithmic functions and the exponential model
Tangent lines to parametric equations and related rates examples
What the derivatives of a function tell us about the shape of its graph
Optimizing values in word problems
Examples finding a volume using disks, washers, and by slicing
Finding the point where two lines in three-dimensional space intersect
Finding an equation of the plane containing two given lines in three-dimensional space
Identifying the equation of a hyperboloid and sketching its graph
Evaluating a line integral along a curve in space
Finding the slope of solutions and the critical points of a differential equation
Finding when the tangent line to a function is horizontal in Python
Using Python to plot an implicit curve and find a tangent line using implicit differentiation
Finding the domain of a function with a denominator, square root, and logarithm
Finding the domain of a function with a natural logarithm and denominator
Finding the domain of a function with a square root in the denominator
Finding the domain of a function with a root and a logarithm in the denominator
Finding the domain of a logarithmic function
Finding the domain of even and odd roots
Finding the domain of functions with even and odd roots
Finding the domain of several rational functions
Finding the domain of a rational function
Explaining how to find any holes and vertical asymptotes of a rational function
Finding the domain of a rational function using factoring
Explaining domain restrictions for denominators, even roots, and logarithms
Explaining the standard form for a quadratic equation and the possible number of solutions
Solving quadratic equations with the difference of two squares formula
Solving quadratic equations by factoring
Solving a quadratic equation by factoring
Solving a quadratic equation by factoring
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Explaining when a quadratic equation does not have a real solution
Explaining the graph and properties for the parent function of quadratics
Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
Explaining the general properties of even and odd root functions
How to rewrite radical terms as power terms
Explaining how to solve radical equations and then solving example problems
Solving equations with even roots and checking the solutions
Solving equations with odd radicals
Solving equations with multiple radicals
Properties of exponents applied to power and exponential expressions
Properties of multiplying and simplifying power and exponential expressions
Properties of exponents applied to power and exponential expressions
Properties of exponential growth and decay functions
Properties of the exponential function with base e
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Simplifying an expression with both power and exponential functions using properties of exponents
Explaining how to solve equations with power and exponential terms
Solving equations with exponential terms
Solving equations with base e exponential terms
Explaining the terminology and rules of logarithms
Explaining the basic properties of logarithmic functions
Expanding logarithmic expressions using logarithm rules
Condensing a logarithmic expression into a single logarithm
Explaining how to solve logarithmic equations
Solving logarithmic equations with a single logarithm term
Solving logarithmic equations with multiple logarithm terms
Solving logarithmic equations with multiple logarithm terms on both sides
Discussing parent functions of rational functions and their properties
Finding horizontal asymptotes for rational functions
Explaining how to do polynomial long division
Finding horizontal asymptotes for rational functions
Determining the end behavior and horizontal asymptotes for rational functions
Explaining basic algebraic operations for fractions
How to simplify rational expressions
Adding and subtracting rational expressions by finding a common denominator
Explaining how to multiply and divide rational expressions
Performing algebraic operations with rational expressions and simplifying the answer
Solving equations that contain rational expressions
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions
Explanation of partial derivatives for functions with more than one variable
Finding the partial derivatives of a function
Finding the partial derivatives of a function with two variables
Example of finding a partial derivative of a function with two variables
Explaining tangent planes for functions of two variables and how to calculate them
Explanation of partial derivatives for functions with more than one variable
Explaining tangent planes for functions of two variables and how to calculate them
Explaining the notation used for statistics and parameter for mean, standard deviation, variance, proportion, and slope