Estas son la mayoría de las transparencias de mi curso de Cálculo Diferencial del semestre Agosto-diciembre de 2012.

1. Week 3
1. Opener.
Answer the following
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2. 2. What is a logarithm?
Remember that
means “to what power should I rise a to get b”.
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3. 2. Logarithmic Equations.
Solve the equations
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4. 2. Logarithmic Equations.
Solve the equations
x=8
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5. 2. Logarithmic Equations.
Solve the equations
x=8
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6. 2. Logarithmic Equations.
Solve the equations
x=8
x = 11/2
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7. 2. Logarithmic Equations.
Solve the equations
x=8
x = 11/2
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8. 2. Logarithmic Equations.
Solve the equations
x=8
x = 11/2
x = e-1/2
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9. 3. Exponential Equations.
Solve the equations
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10. 3. Exponential Equations.
Solve the equations
x=4
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11. 3. Exponential Equations.
Solve the equations
x=4
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12. 3. Exponential Equations.
Solve the equations
x=4
x = -1
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13. 3. Exponential Equations.
Solve the equations
x=4
x = -1
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14. 3. Exponential Equations.
Solve the equations
x=4
x = -1
x=3
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15. 4. Basic Graphs of Functions.
Sketch the graph of the following functions.
1. y = x
2. y = x 2
3. y = x 3
4. y = x 4
5. y = 1
x
6. y = x
7. y = 3 x
8. y = x
9. y = a x
10. y = log a x
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16. viernes, 24 de agosto de 12

17. 1. Exercise.
Sketch the following functions. Find the domain, range and asymptotes (if
any).
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18. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a
2. f(x) - a
3. f(x + a)
4. f(x - a)
5. - f(x)
6. f(-x)
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19. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a
3. f(x + a)
4. f(x - a)
5. - f(x)
6. f(-x)
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20. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a)
4. f(x - a)
5. - f(x)
6. f(-x)
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21. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a)
5. - f(x)
6. f(-x)
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22. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a) Shifted right a units
5. - f(x)
6. f(-x)
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23. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a) Shifted right a units
5. - f(x) Reflected about the x-axis
6. f(-x)
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24. 2. Transformation of Functions.
If we have a function f(x), what happens if we have
1. f(x) + a Shifted upward a units
2. f(x) - a Shifted downward a units
3. f(x + a) Shifted left a units
4. f(x - a) Shifted right a units
5. - f(x) Reflected about the x-axis
6. f(-x) Reflected about the y-axis
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25. 3. Homework 3
Blackboard -> Assignments
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26. Practice with Graphical Analysis
Domain
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27. Practice with Graphical Analysis
Domain =R
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28. Practice with Graphical Analysis
Domain =R
Range
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29. Practice with Graphical Analysis
Domain =R
Range =
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30. Practice with Graphical Analysis
Domain =R
Range =
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31. Practice with Graphical Analysis
Evaluate f(0)
Evaluate f(0) - f(1)
Evaluate f(f(0))
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32. Practice with Graphical Analysis
Evaluate f(0) =3
Evaluate f(0) - f(1)
Evaluate f(f(0))
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33. Practice with Graphical Analysis
Evaluate f(0) =3
Evaluate f(0) - f(1) = 3 - 2 = 1
Evaluate f(f(0))
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34. Practice with Graphical Analysis
Evaluate f(0) =3
Evaluate f(0) - f(1) = 3 - 2 = 1
Evaluate f(f(0)) = f(3) = -6
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35. Practice with Graphical Analysis
Solve for x: f(x) < -4
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36. Practice with Graphical Analysis
Solve for x: f(x) < -4
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37. Practice with Graphical Analysis
Solve for x: f(x) < -4 (2, 4)
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38. Practice with Graphical Analysis
Solve for x: f(x) < -4 (2, 4)
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39. Practice with Graphical Analysis
Solve for x: f(x) < -4 (2, 4)
Solve for x: f(x) 2
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40. Practice with Graphical Analysis
Solve for x: f(x) < -4 (2, 4)
Solve for x: f(x) 2
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41. Practice with Graphical Analysis
Solve for x: f(x) < -4 (2, 4)
Solve for x: f(x) 2
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42. Practice with Graphical Analysis
Solve for x: f(x) < -4 (2, 4)
Solve for x: f(x) 2 [-1, 1]
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43. Homework 4
Blackboard -> Assignments
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