1. Homework Homework Assignment #16 Read Section 3.8
Page 178, Exercises: 1 – 93 (EOO)
Quiz next time
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2. Example, Page 178 Fill in the table. Rogawski Calculus
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3. Example, Page 178
Write the function as a composition and find the derivative.
Rogawski Calculus
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4. Example, Page 178 Find the derivative. Rogawski Calculus
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5. Example, Page 178 Find the derivative. Rogawski Calculus
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6. Example, Page 178 Find the derivative of f ○ g. 17. Rogawski Calculus
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7. Example, Page 178 Find the derivative. 21. Rogawski Calculus
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8. Example, Page 178 Find the derivative. 25. Rogawski Calculus
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9. Example, Page 178 Find the derivative. 29. Rogawski Calculus
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10. Example, Page 178 Find the derivative. 33. Rogawski Calculus
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11. Example, Page 178 Find the derivative. 37. Rogawski Calculus
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12. Example, Page 178 Find the derivative. 41. Rogawski Calculus
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13. Example, Page 178 Find the derivative. 45. Rogawski Calculus
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14. Example, Page 178 Find the derivative. 49. Rogawski Calculus
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15. Example, Page 178 Find the derivative. 53. Rogawski Calculus
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16. Example, Page 178 Find the derivative. 57. Rogawski Calculus
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17. Example, Page 178 Find the derivative. 61. Rogawski Calculus
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18. Example, Page 178 Find the derivative. 65. Rogawski Calculus
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19. Example, Page 178 Find the derivative. 69. Rogawski Calculus
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20. Example, Page 178 73. Rogawski Calculus
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21. Example, Page 178 77. Rogawski Calculus
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22. Example, Page 178
Use the table of values to calculate the derivative of the function at the given point. 81.
Rogawski Calculus
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23. Example, Page 178 Compute the indicated higher derivatives. 85.
Rogawski Calculus
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24. Example, Page 178 89. Rogawski Calculus
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25. Example, Page 178
93. The force F (Newtons) between two charged particles is F = 100/r2, where r is the distance (meters) between them. Find dF/dt at t = 10 if distance at time t (sec) is r = t2.
Rogawski Calculus
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26. Chapter 3: Differentiation Section 3.8: Implicit Differentiation
Jon Rogawski Calculus, ET First Edition
Chapter 3: Differentiation
Section 3.8: Implicit Differentiation
Rogawski Calculus
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27. The graph in Figure 1 is not that of a function, but of a relation. It
is said that y is defined implicitly, as it could be difficult or
impossible to solve the equation for y. To find the slope of the
tangent line, we must use implicit differentiation.
Rogawski Calculus
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28. in question? Consider the equation for the unit circle x2 + y2 = 1.
Consider the unit
circle shown in Figure 2.
How do we determine
the slope at the point
in question? Consider the
equation for the unit
circle x2 + y2 = 1.
Rogawski Calculus
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29. The relation y4 + xy = x3 – x + 2 may be broken down into two
functions, each defining a branch of the curve and neither
violating the vertical line rule. The point where the branches split
is the point at which the curve has a vertical slope.
Rogawski Calculus
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30. Find the equation of the tangent to the curve y4 + xy = x3 – x + 2
Rogawski Calculus
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31. Rogawski Calculus
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32. Rogawski Calculus
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33. Rogawski Calculus
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34. Homework Homework Assignment #17 Read Section 3.9
Page 184, Exercises: 1 – 49 (EOO)
Rogawski Calculus
Copyright © 2008 W. H. Freeman and Company