Embedded Files
Opening Day Handout
General Timeline (with "drill-down" topics) Link to Document
Unit 1 - Functions (review of previous courses)
Lesson 1 Function Notation and Rates of Change Blank Notes | Completed Notes
In this lesson, we will Interpret and use function notation, write and simplify difference quotients given function notation, calculate the average rate of change of a function over an interval, define a secant line as a line connecting any two points on a curve, and write the equation of a secant line of a function in point-slope form.
Lesson 2 Representing Functions Blank Notes | Completed Notes
Today we will sketch the graph of parent functions (constant, linear, absolute value, quadratic, cubic, square root, exponential, logarithmic, piecewise functions); define power functions, root functions, and rational functions; identify features of the parent functions (name, equation, domain, range, increasing intervals, decreasing intervals, relative maximums or minimums, end behavior); and sketch basic transformations of the parent functions
Quiz to follow Review of Selected Topics
Unit 2 - Limits
Lesson 2 Definitions of Limits Blank Notes | Completed Notes
Today we will define the limit of a function, define left-hand and right-hand limits, define when a limit does not exist, evaluate limits based on the graph of a function, evaluate limits using direct substitution, evaluate limits using TI-Nspire, and sketch the graph of a function given limits and function values.
Lesson 3 Techniques for Computing Limits (part 1) Blank Notes | Completed Notes
Lesson 3 Techniques for Computing Limits (part 2) Blank Notes | Completed Notes
Taken together, Lesson 3 incorporates defining the Basic Limit Laws, using those laws to evaluate the limit of an unknown function based on table of values, defining indeterminate forms, and evaluating limits algebraically when direct substitution results in 0/0 (factor and simplify, polynomial division, rationalize, simplify complex fractions, basic trigonometric identities).
Quiz or Graded Classwork to follow
Lesson 4 Infinite Limits Blank Notes | Completed Notes
Today we will visually identify limits that approach infinity, define vertical asymptote using limits, evaluate limits that approach infinity of rational functions by hand using numerical methods, and identify the location of vertical asymptotes of rational functions using limits.
Lesson 5 Limits at Infinity Blank Notes | Completed Notes
Today we will review end behavior of polynomial functions and basic rational functions from Algebra 2 to relate it to limits as x approaches infinity in Calculus, define horizontal asymptotes using limits, evaluate the limit as x approaches infinity of rational functions, and use limits to identify the existence/location of horizontal asymptote of rational functions.
Quiz to follow
Lesson 6 Continuity Blank Notes | Completed Notes
In today's lesson we will define continuity of a function, define three part criteria for a function to be continuous using limits, define three types of discontinuities (removable, jump, infinite), visually identify the location of discontinuities of a function from a graph, use the three criteria for continuity to discuss the continuity of a function given its equation, and find the values of the variables that would make the function continuous at a given point.
DeltaMath graded assignment to follow
Unit 3 - Derivatives
Desmos applet #1 - Secant Line ---> Tangent Line
This applet demonstrates how reducing the distance between two points, a and b, causes the secant line through (a, f(a)) and (b, f(b)) to “morph” into the tangent line at (a, f(a)). Feel free to save a copy and experiment with different functions and values of a and b!
Lesson 1 Introducing the Derivative Blank Notes | Completed Notes | Video Explaining IRC formulas
Today we will recap average rate of change, definition of secant line, writing the equation of the secant line, describe how a secant line approaches a tangent line as the x coordinates approach each other, define tangent line and the equation of a tangent line in point slope form, define the derivative as the IRC of a curve at a point -or- the slope of a tangent line at that point -or-the slope of the curve at that point. We'll also demonstrate that the limit of the ARC produces the instantaneous rate of change. Finally, we will use the limit definition of a derivative at a point, both x approaches a and h approaches 0 definition, to calculate the derivatives of various functions and define prime notation.
Lesson 2 The Derivative as a Function [Day 1] Blank Notes | Completed Notes
In this lesson we will define differential operator notation, visualize the derivative as a function and interpret the meaning of the points on the graph of the derivative, define the limit definition of the derivative as a function which can be evaluated at any point where the derivative exists, define differentiation, aind find the derivative of various functions (polynomials, radicals, rational functions) as a function.
Desmos applet #2 - Evaluating f'(x) at various a-values
This applet will draw various tangent lines to the function of your choice at the a-values of your choice. You can use the value of f'(a) to visually verify the slopes of the tangent lines.
Derivative Skill Check
This is the assignment given during my absence on 10/17 Completed Problems
Lesson 2 The Derivative as a Function [Day 2] Blank Notes | Completed Notes
In this lesson we will deduce what the graph of f' might look like if we know what the graph of f looks like. As an extension, we'll try to make connections between key feature of a the graph of f compared to the behavior of f'. Finally, we'll determine where functions do not have a derivative, based solely on the "shape" of the graph.
Here is a supplement to use limits to explain nondifferentiability. Supplement | Completed
Quiz after these topics Review of Topics | Completed
Lesson 3 Rules of Differentiation [Day 1] Blank Notes | Completed Notes
In this lesson, we develop rules for taking derivatives without having to rely on the tedium of using the limit definition! Specifically, we learned the Constant Rule, Power Rule, Constant Multiple Rule, and the Sum Rule.
Lesson 3 Rules of Differentiation [Day 2] Blank Notes | Completed Notes
In this lesson, we develop rules taking the derivative of the natural exponential function. We'll also introduce the concept of higher-order derivatives, which are derivatives of derivative functions.
Lesson 4 The Product and Quotient Rules Blank Notes | Completed Notes & Homework
Today, we examine special rules for taking the derivative of a function that is expressed as a product or quotient of two or more functions.
Quiz after these topics
Lesson 5 Derivatives of Trigonometric Functions Blank Notes | Completed Notes
Practice Problems | Completed Practice Problems
Today, we’ll explore some interesting trigonometric limits involving sine and cosine. Then we’ll learn the derivatives of the sine and cosine functions and use them to develop the derivatives of the other four trigonometric functions. Finally, we’ll apply previously learned rules to differentiate products and quotients of these functions, as well as compute higher-order derivatives.
Lesson 6 Derivatives as Rates of Change Blank Notes | Completed Notes
In today's lesson, we will examine the relationship between position, velocity, and acceleration. We'll also talk about such concepts as displacement and average velocity. We will examine these from an analytical and graphical point of view.
Lesson 7 The Chain Rule [Day 1] Blank Notes | Completed Notes
The Chain Rule [Day 2] Blank Notes | Completed Notes
In today's lesson, we'll reivew what it means to take the composition of two functions, and we'll practice a rule that allows us to take the derivative of a function that is expressed as a composition of functions.
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