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# DiffCalculus Week 3

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

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### DiffCalculus Week 3

1. 1. Week 3 1. Opener. Answer the followingviernes, 24 de agosto de 12
2. 2. 2. What is a logarithm? Remember that means “to what power should I rise a to get b”.viernes, 24 de agosto de 12
3. 3. 2. Logarithmic Equations. Solve the equationsviernes, 24 de agosto de 12
4. 4. 2. Logarithmic Equations. Solve the equations x=8viernes, 24 de agosto de 12
5. 5. 2. Logarithmic Equations. Solve the equations x=8viernes, 24 de agosto de 12
6. 6. 2. Logarithmic Equations. Solve the equations x=8 x = 11/2viernes, 24 de agosto de 12
7. 7. 2. Logarithmic Equations. Solve the equations x=8 x = 11/2viernes, 24 de agosto de 12
8. 8. 2. Logarithmic Equations. Solve the equations x=8 x = 11/2 x = e-1/2viernes, 24 de agosto de 12
9. 9. 3. Exponential Equations. Solve the equationsviernes, 24 de agosto de 12
10. 10. 3. Exponential Equations. Solve the equations x=4viernes, 24 de agosto de 12
11. 11. 3. Exponential Equations. Solve the equations x=4viernes, 24 de agosto de 12
12. 12. 3. Exponential Equations. Solve the equations x=4 x = -1viernes, 24 de agosto de 12
13. 13. 3. Exponential Equations. Solve the equations x=4 x = -1viernes, 24 de agosto de 12
14. 14. 3. Exponential Equations. Solve the equations x=4 x = -1 x=3viernes, 24 de agosto de 12
15. 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 xviernes, 24 de agosto de 12
16. 16. viernes, 24 de agosto de 12
17. 17. 1. Exercise. Sketch the following functions. Find the domain, range and asymptotes (if any).viernes, 24 de agosto de 12
18. 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)viernes, 24 de agosto de 12
19. 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)viernes, 24 de agosto de 12
20. 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)viernes, 24 de agosto de 12
21. 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)viernes, 24 de agosto de 12
22. 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)viernes, 24 de agosto de 12
23. 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)viernes, 24 de agosto de 12
24. 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-axisviernes, 24 de agosto de 12
25. 25. 3. Homework 3 Blackboard -> Assignmentsviernes, 24 de agosto de 12
26. 26. Practice with Graphical Analysis Domainviernes, 24 de agosto de 12
27. 27. Practice with Graphical Analysis Domain =Rviernes, 24 de agosto de 12
28. 28. Practice with Graphical Analysis Domain =R Rangeviernes, 24 de agosto de 12
29. 29. Practice with Graphical Analysis Domain =R Range =viernes, 24 de agosto de 12
30. 30. Practice with Graphical Analysis Domain =R Range =viernes, 24 de agosto de 12
31. 31. Practice with Graphical Analysis Evaluate f(0) Evaluate f(0) - f(1) Evaluate f(f(0))viernes, 24 de agosto de 12
32. 32. Practice with Graphical Analysis Evaluate f(0) =3 Evaluate f(0) - f(1) Evaluate f(f(0))viernes, 24 de agosto de 12
33. 33. Practice with Graphical Analysis Evaluate f(0) =3 Evaluate f(0) - f(1) = 3 - 2 = 1 Evaluate f(f(0))viernes, 24 de agosto de 12
34. 34. Practice with Graphical Analysis Evaluate f(0) =3 Evaluate f(0) - f(1) = 3 - 2 = 1 Evaluate f(f(0)) = f(3) = -6viernes, 24 de agosto de 12
35. 35. Practice with Graphical Analysis Solve for x: f(x) < -4viernes, 24 de agosto de 12
36. 36. Practice with Graphical Analysis Solve for x: f(x) < -4viernes, 24 de agosto de 12
37. 37. Practice with Graphical Analysis Solve for x: f(x) < -4 (2, 4)viernes, 24 de agosto de 12
38. 38. Practice with Graphical Analysis Solve for x: f(x) < -4 (2, 4)viernes, 24 de agosto de 12
39. 39. Practice with Graphical Analysis Solve for x: f(x) < -4 (2, 4) Solve for x: f(x) 2viernes, 24 de agosto de 12
40. 40. Practice with Graphical Analysis Solve for x: f(x) < -4 (2, 4) Solve for x: f(x) 2viernes, 24 de agosto de 12
41. 41. Practice with Graphical Analysis Solve for x: f(x) < -4 (2, 4) Solve for x: f(x) 2viernes, 24 de agosto de 12
42. 42. Practice with Graphical Analysis Solve for x: f(x) < -4 (2, 4) Solve for x: f(x) 2 [-1, 1]viernes, 24 de agosto de 12
43. 43. Homework 4 Blackboard -> Assignmentsviernes, 24 de agosto de 12

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Apr. 10, 2021

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

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