Differential Calculus

Omar G. Monteagudo, Sep 15, 2020

Table of Contents

  1. Limits
    1. The limit of a real function - Numerical approximation: Formative assessment
    2. The limit of a constant function
    3. The limit of the identity function
    4. The limit of a polynomial function
    5. The limit of a rational function
    6. The limit of a piecewise-defined function
    7. The limit of a polynomial function: formative assessment
  2. Derivatives
    1. The derivative of a function as a rate of change
    2. The derivative of a polynomial function
  3. Optimization
    1. Volume of a lidless box

1.

Limits

  • 1. The limit of a real function - Numerical approximation: Formative assessment
  • 2. The limit of a constant function
  • 3. The limit of the identity function
  • 4. The limit of a polynomial function
  • 5. The limit of a rational function
  • 6. The limit of a piecewise-defined function
  • 7. The limit of a polynomial function: formative assessment

1.1.

The limit of a real function - Numerical approximation: Formative assessment

– Omar G. Monteagudo

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Derivatives

  • 1. The derivative of a function as a rate of change
  • 2. The derivative of a polynomial function

2.1.

The derivative of a function as a rate of change

– Omar G. Monteagudo

2.2.

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3.

Optimization

  • 1. Volume of a lidless box

3.1.

Volume of a lidless box

Instructions
1. Slide the red point and learn how the volume of the box varies as the length of the red squares in the corners of the sheet of paper varies.[br]2. Slide the black point named "Faces" to learn how the box is built one the corners are cut into four congruent squares.[br]3. Let [math]x[/math] be the length of the sides of the squares cut in the corners of the sheet of paper. Write the polynomial function [math]V\left(x\right)[/math] which describes the volume of the box built in this way. What is its domain (in this context)? What is its range (in this context)?
– Omar G. Monteagudo

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