~~META:title=Limits: Flipped Calculus at Binghamton SUNY~~
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===== The Limit of a Function =====
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//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]]
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===== Tangents, Derivatives, and Rates of Change =====
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//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]]
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===== Limit Laws =====
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//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]]
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===== Continuity =====
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//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]]
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