Limits: Flipped Calculus at Binghamton SUNY [Department of Mathematics and Statistics, Binghamton University]

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<h1 style=“margin-top:1; margin-bottom:1;”>Flipped Calculus 1 at Binghamton</h1>

<ul> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources”>Home</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/limits”>Limits</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/derivatives”>Derivatives</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications”>Applications</a></li> <li><a href=“http://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals”>Integrals</a></li> </ul>

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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.

Classroom Slides PDF

Classroom Slides TEX

===== 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.

Classroom Slides PDF

Classroom Slides TEX

===== 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.

Classroom Slides PDF

Classroom Slides TEX

===== 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).

Classroom Slides PDF

Classroom Slides TEX

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<h1>Laura Anderson and Joseph Brennan</h1>

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