Khan Academy Calculus BC and Math 201
Look over, watch, and attempt some problems from the indicated sections in Khan Academy's Calc BC. Do not watch all of the videos since we will not cover all topics in calculus BC this semester in math 201. I've made a dictionary between sections in Khan Academy's course with the corresponding sections in our textbook that we will be studying in 201. You can even attempt some of the Khan Academy quizzes for extra practice.
Khan Academy Unit 1 Limits and Continuity (Chapter 2 in our text).
Defining limits and using limit notation overlaps with section 2.2 The Limit of a Function from our textbook.
Estimating limit values from graphs overlaps with section 2.2 The Limit of a Function from our textbook.
Estimating limit values from tables overlaps with section 2.2 The Limit of a Function from our textbook.
Determining limits using algebraic properties of limits: limit properties overlaps with section 2.3 Calculating Limits Using the Limit Laws from our textbook.
Determining limits using algebraic properties of limits: direct substitution overlaps with section 2.3 Calculating Limits Using the Limit Laws from our textbook.
Determining limits using algebraic manipulation overlaps with section 2.3 Calculating Limits Using the Limit Laws from our textbook.
Selecting procedures of determining limits overlaps with section 2.3 Calculating Limits Using the Limit Laws from our textbook.
Determining limits using the squeeze theorem overlaps with section 2.3 Calculating Limits Using the Limit Laws from our textbook.
Exploring Types of discontinuities overlaps with section 2.5 Continuity from our textbook.
Defining continuity at a point overlaps with section 2.5 Continuity from our textbook.
Confirming continuity over an interval overlaps with section 2.5 Continuity from our textbook.
Removing discontinuities overlaps with section 2.5 Continuity from our textbook.
Connecting infinite limits and vertical asymptotes overlaps with section 2.3 Calculating Limits Using the Limit Laws from our textbook.
Connecting infinite limits and horizontal asymptotes overlaps with section 2.6 Limits at Infinity Horizontal Asymptotes from our textbook.
Working with the intermediate value theorem overlaps with section 2.5 Continuity from our textbook.
Khan Academy Unit 2 Differentiation Basics (Chapters 2 and 3 of our text).
Defining average and instantaneous rates of change at a point overlaps with section 2.1 Tangent and Velocity Problems from our textbook.
Defining the derivative as a function using derivative notation overlaps with section 2.8 The Derivative as a Function from our textbook.
Estimating derivatives of a function at a point overlaps with section 2.1 Tangent and Velocity Problems from our textbook.
Connecting differentiability and continuity: determining when derivatives do and do not exist overlaps with section 2.8 The Derivative as a Function from our textbook.
Applying the Power Rule overlaps with section 3.1 Derivatives of Polynomial and Exponential Functions from our textbook.
Derivative Rules: constant sum, difference, and constant multiple: intro overlaps with section 3.1 Derivatives of Polynomial and Exponential Functions from our textbook.
Derivative Rules: constant sum, difference, and constant multiple: connecting with the power rule overlaps with section 3.1 Derivatives of Polynomial and Exponential Functions from our textbook.
Derivatives of cos(x), sin(x), e^x, and ln(x) overlaps with section 3.1 (e^x), 3.3 (trig functions), and 3.6 (ln) from our textbook.
The product rule overlaps with section 3.2 The Product and Quotient Rules from our textbook.
The quotient rule overlaps with section 3.2 The Product and Quotient Rules from our textbook.
Finding derivatives of tangent, cotangent, secant, and/or cosecant functions overlaps with section 3.3 Derivatives of Trig Functions from our textbook.
Unit 3 Differentiation: composite, implicit, and inverse functions (Chapter 3 of our text).
The Chain Rule: introduction overlaps with section 3.4 The Chain Rule from our textbook.
The Chain Rule: further practice overlaps with section 3.4 The Chain Rule from our textbook.
Implicit Differentiation overlaps with section 3.5 Implicit Differentiation from our textbook.
Differentiating inverse functions skip this Khan Academy section.
Differentiating inverse trig functions overlaps with section 3.6 Derivatives of Logs and Inverse Trig Functions from our textbook.
Selecting procedures for calculating derivative: strategy overview of *Chapter 3 Differentiating Rules: from our textbook.
Selecting procedures for calculating derivative: multiple rules overview of *Chapter 3 Differentiating Rules: from our textbook.
Calculating higher order derivatives overview of *Chapter 3 Differentiating Rules: from our textbook.
Further practice connecting derivatives and limits skip this Khan Academy section.
Khan Academy Unit 4 Applications of Differentiation (Chapters 3 and 4 of our text).
Straight line motion: connecting position, velocity, and acceleration overlaps with section 3.7 Rates of Change in Sciences from our textbook.
Introduction to Related Rates + Solving Related Rates problems overlaps with section 3.9 Related Rates from our textbook.
Approximating values of a function using local linearity and linearization overlaps with section 3.10 Linear Approximation and Differentials from our textbook.
Using L'Hopital's rule for finding limits of indeterminate forms overlaps section 4.4 Indeterminate Forms and L'Hospital's Rule from our text.
Khan Academy Unit 5 Applying Derivatives to analyze functions (Chapter 4 of our text).
Using the mean value theorem overlaps with section 4.2 The Mean Value Theorem from our textbook.
Extreme value theorem, global versus local extrema, and critical points overlaps with section 4.1 Maximum and Minimum Values from our textbook.
Determining intervals on which a function is increasing or decreasing overlaps with section 4.3 What Derivatives Tell Us About the Shape of a Graph from our textbook.
Using the first derivative test to find relative (local) extrema overlaps section 4.1 Maximum and Minimum Vales from our text.
Using the candidates test to find absolute (global) extrema overlaps with section 4.1 Maximum and Minimum Vales from our text.
Determining concavity of intervals and finding points of inflection: graphical + algebraic overlaps with section 4.3 What Derivatives Tell Us About the Shape of a Graph from our textbook.
Using the second derivative test to find extrema overlaps with section 4.3 What Derivatives Tell Us About the Shape of a Graph from our textbook.
Solving optimization problems overlaps with section 4.7 Optimization Problems from our textbook.
