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CALCULUS I MATH 181 |
Southwestern Adventist University |
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| Distance Education | Lawrence E. Turner, Jr., Ph.D. | |
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(Thomas and Finney, 9th edition)
Chapter 2 Derivatives
9. Using the definition (as a limit involving h), calculate the derivative of the following functions:
- hint, rationalize the numerator
(10)
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(5)
10. Find the slope of the tangent line of the following function at the indicated point.
(5)
11. For the following functions find the first and second derivatives:
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(10)
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(10)
12. It takes 12 hours to drain a storage tank by opening the valve at the bottom. The depth y of the fluid in the tank t hours after the value is opened is given by:
- Find the rate dy/dt (in meters/hours) at which the tank is draining at time t.
(5)
- When is the fluid level in the tank falling fastest? slowest?
(5)
13. For the following find dy/dx:
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(10)
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(10)
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(10)
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(10)
14. Use implicit differentiation to find dy/dx for the following:
(10)
15. Suppose that the radius r and area A = r2 of a circle are differentiable functions of t. Write an equation that relates dA/dt to dr/dt.
(5)
© 1999, 2000, 2001, 2002, 2003, 2008 by Lawrence Turner