~~META:title=Limits: Flipped Calculus at Binghamton SUNY~~ ~~NOTOC~~ \\ ===== The Limit of a Function ===== {{youtube>vaZfqpWYDO8}} //Section 1.5 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * The limit at an x-value describes the y-value the function "approaches" at that x-value.\\ * Graphical intuition for limits.\\ * Two-sided limits depend on both one-sided limits. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.5_limit.pdf|Classroom Slides PDF]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.5_limit_tex|Classroom Slides TEX]] \\ ===== Tangents, Derivatives, and Rates of Change ===== {{youtube>oqBLj4coFvg}} {{youtube>9_3l1bqV4Ak}} \\ //Section 1.4/2.1 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * A rate of change describes how one quantity changes in relation to another quantity.\\ * Rate of change can result from averaging over an interval or finding a limit of averages approaching a single point.\\ * Tangent lines result from the limit of secant lines.\\ * A derivative is an instantaneous rate of change. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.4-2.1_rates_of_change.pdf|Classroom Slides PDF]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.4-2.1_rates_of_change_tex|Classroom Slides TEX]] \\ ===== Limit Laws ===== {{youtube>jeiF2tm4Wx4}} {{youtube>7RZJSTJQL5E}} \\ //Section 1.6 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * Algebraic limit laws.\\ * When direct substitution isn't allowable in calculating a limit try simplification, conjugation, or squeezing the function. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.6_limit_laws.pdf|Classroom Slides PDF]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.6_limit_laws_tex|Classroom Slides TEX]] \\ ===== Continuity ===== {{youtube>h836P0BCEcI}} {{youtube>sb13L83w0n0}} \\ {{youtube>75Q69ZyOz5c}} //Section 1.8 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * Graphical intuition of continuity.\\ * Where limits align with actual values, a function is continuous.\\ * Types of discontinuities.\\ * Algebraic limit laws.\\ * Continuous functions cannot jump (Intermediate Value Theorem). [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/1.8_continuity.pdf|Classroom Slides PDF]]\\ \\ [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits/1.8_continuity_tex|Classroom Slides TEX]] \\