Cálculo I

Geogebra Cumbres, Aug 23, 2016

Math 5th Semester Prepa Tec Campus Cumbres

Table of Contents

  1. Limits and Continuity
    1. Limits: Introductory Questions
    2. Limits: Introductory Questions (2)
    3. Estimating slope of a tangent line using a secant line
    4. Explore Limit Graphically And Numerically
    5. One-sided limits
    6. Graphical Limits
    7. Infinite Limits and Limits at Infinity
    8. grapher with many features
    9. Limits at Infinity 8
    10. Limits at Infinity 1
    11. Infinite limits
    12. more infinite limits
    13. Continuity and Differentiability
    14. Continuity 1
    15. Continuity 3
  2. The Derivative
    1. Graphing The Derivative of a Function
    2. Graphs of Derivative Functions
    3. Tangent Lines and Derivatives
    4. Derivative , and Tangent line, for a cubic
    5. tangent and derivative
  3. Differentiation rules and applications
    1. Product & Quotient Rules of Differentiation
    2. Basic Differentiation Self Practice Sheet
    3. Differentiation with Chain Rule Self Practice Sheet
    4. Differentiation using Quotient Rule Self Practice Sheet
    5. Differentiation using Product Rule Self Practice Sheet
    6. Graphing The Derivative of a Function
    7. Higher Order Derivatives - Demo
    8. Implicit Differentiation
    9. Example of Implicit Differentiation
    10. Related Rates: Filling/Draining Cone (II)
    11. Differentiation from First Principles
  4. Analysis of Functions using derivates
    1. Derivative of Tangent Function (Investigation)
    2. Derivative of Natural Log Function
    3. Graphing The Derivative of a Function
    4. Sketch the Derivative (Warm Up)
    5. Minimizing the Area of a Triangle
    6. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
    7. Optimization Challenge 1

1.

Limits and Continuity

  • 1. Limits: Introductory Questions
  • 2. Limits: Introductory Questions (2)
  • 3. Estimating slope of a tangent line using a secant line
  • 4. Explore Limit Graphically And Numerically
  • 5. One-sided limits
  • 6. Graphical Limits
  • 7. Infinite Limits and Limits at Infinity
  • 8. grapher with many features
  • 9. Limits at Infinity 8
  • 10. Limits at Infinity 1
  • 11. Infinite limits
  • 12. more infinite limits
  • 13. Continuity and Differentiability
  • 14. Continuity 1
  • 15. Continuity 3

1.1.

Limits: Introductory Questions

The questions you need to answer are contained in the applet below.
– Tim Brzezinski

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1.7.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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2.

The Derivative

  • 1. Graphing The Derivative of a Function
  • 2. Graphs of Derivative Functions
  • 3. Tangent Lines and Derivatives
  • 4. Derivative , and Tangent line, for a cubic
  • 5. tangent and derivative

2.1.

Graphing The Derivative of a Function

[color=#000000]Remember: The derivative of a function [i]f[/i] at [i]x[/i] = [i]a[/i], if it even exists at [i]x[/i] = [i]a[/i], can be geometrically interpreted as the slope of the tangent line drawn to the graph of [i]f[/i] at the point ([i]a, f(a))[/i]. [br][br]Hence, the [/color][color=#ff00ff]y-coordinate (output) of the pink point = the slope of the tangent line [/color][color=#000000]drawn to the graph of [i]f[/i] at the [/color][b][color=#000000]BIG BLACK POINT[/color][/b][color=#000000]. (Note that the [/color][b][color=#ff00ff]pink point[/color][/b][color=#000000] and the [b]BLACK POINT[/b] always have the same x-coordinate.) [/color]
– Tim Brzezinski

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2.5.

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3.

Differentiation rules and applications

  • 1. Product & Quotient Rules of Differentiation
  • 2. Basic Differentiation Self Practice Sheet
  • 3. Differentiation with Chain Rule Self Practice Sheet
  • 4. Differentiation using Quotient Rule Self Practice Sheet
  • 5. Differentiation using Product Rule Self Practice Sheet
  • 6. Graphing The Derivative of a Function
  • 7. Higher Order Derivatives - Demo
  • 8. Implicit Differentiation
  • 9. Example of Implicit Differentiation
  • 10. Related Rates: Filling/Draining Cone (II)
  • 11. Differentiation from First Principles

3.1.

Product & Quotient Rules of Differentiation
– MrQuinn

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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4.

Analysis of Functions using derivates

  • 1. Derivative of Tangent Function (Investigation)
  • 2. Derivative of Natural Log Function
  • 3. Graphing The Derivative of a Function
  • 4. Sketch the Derivative (Warm Up)
  • 5. Minimizing the Area of a Triangle
  • 6. Optimization: Maximizing Area of a Rectangle Inside a Right Triangle
  • 7. Optimization Challenge 1

4.1.

Derivative of Tangent Function (Investigation)

Displayed below is the graph of [math]f\left(x\right)=tan\left(x\right)[/math]. [br][br]The [b][color=#0000ff]y-coordinate of the [/color][/b][color=#0000ff][b]blue point[/b] [b]= the slope of the line tangent to the graph of [i]f[/i] at the [/b][/color]BIG WHITE POINT. [br][br]Drag this BIG WHITE POINT around to [b][color=#0000ff]observe the graph of the derivative[/color][/b] of function [i]f [/i]being traced out.[br][br]Without opening up another tab in your browser to look it up, feel free to take a guess as to what the derivative of this function might be. (You don't have to do this right away, but you will eventually in the questions that follow.)
1)
Recall the trigonometric identities you've learned previously. Is there a special relationship between the tangent, sine, and cosine of an angle? [br]
2)
Determine the derivative of the function [math]f\left(x\right)=tan\left(x\right)[/math] by applying the quotient rule to the expression you obtained in (1) above.
3)
Rewrite the expression you obtained in (2) so that it's not written as a quotient.
– Tim Brzezinski

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