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

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Course Title: Business Calculus

Lecture Topic: Limits with applications to Business and Economics

Instructor: Jeffrey Castaneda

Institution: Texas A&M International University


Backwards Design

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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.


  • 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:

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?

Model of Knowledge

  • Concept Map
    • Consider the following Graph:


  • Content Priorities
    • Enduring Understanding

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.

    • Important to Do and Know

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.


    • 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

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OBJECTIVE

By the next class period, students will be able to:

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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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