UTPA STEM/CBI Courses/Business Calculus/Limits with applications to Business and Economics

Course Title: Business Calculus

Lecture Topic: Limits with applications to Business and Economics

Instructor: Jeffrey Castaneda

Institution: Texas A&M International University

Backwards Design
Course Objectives


 * Primary Objectives- By the next class period students will be able to:
 * Use the derivative to solve extrema problems (Optimization problems);


 * Sub Objectives- The objectives will require that students be able to:
 * Solving real world problems using derivatives
 * Find absolute maximum or minimum value of a function f.


 * Difficulties- Students may have difficulty:
 * Constructe the needed function to maximize or minimize,and
 * Express the function with multiple variables in terms of a function with one variable as needed.

A load must be suspended 6 m below a high ceiling using cables attached to two supports that are 2m apart. How far below the ceiling x should the cables be joined to minimize the total length of cable used?
 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Engineering
 * Biology
 * Business and Economy
 * Chemistry ...ets
 * Example : Suspension System:

Model of Knowledge


 * Concept Map
 * Consider the following Graph:

1. Understanding the problem: The first step is to read the problem carefully until it is clearly understood. Ask yourself: What is the unknown? What are the given quantities? What are the given conditions? 2. Draw a Diagram: In most of the problems it is useful to draw a diagram and identify the given quantities on the diagram.
 * Content Priorities
 * Enduring Understanding

1. Introduce Notations: Assign a symbol to the quantity that is to be maximized or minimized. For example, A for area, h for height, S for Surface area, V for Volume, ... etc.
 * Important to Do and Know


 * Worth Being Familiar with
 * Formulas related to the given problem.
 * How to find Derivatives and what it means

Assessment of Learning


 * Formative Assessment
 * In Class (groups)
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 * Homework (individual)
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 * Summative Assessment
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Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
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THE CHALLENGE

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GENERATE IDEAS

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MULTIPLE PERSPECTIVES

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RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

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Test Your Mettle Quiz

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