Applied Calculus [enh rvw edn.] by S. Waner, S. Costenoble

By S. Waner, S. Costenoble

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By S. Waner, S. Costenoble

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X y −1 x −1 21. x3 x4 22. y5 y3 23. x 2 y2 x −1 y 24. x −1 y x 2 y2 25. (x y −1 z 3 ) 2 x 2 yz 2 26. x 2 yz 2 (x yz −1 ) −1 27. 28. x 2 y −1 z 0 x yz −2 30. 61. 12. 3 · (−2) 0 17. x 3 x 2 x −1 y −2 z 2 xy 58. 11. 2 · 30 Simplify each expression in Exercises 17–30, expressing your answer in rational form. 29. √ a 2 b2 x y −2 z x −1 z x y −2 x 2 y −1 z 2 x2 71. √ x 2 74. −3 5x 76. 31. 1x −2 + 36. −4 3x 3 34. −3 78. 1 3 32. x −4 33. 3 35. 1 − −2 − x −1 x 5 Evaluate the expressions in Exercises 37–56, rounding your answer to four significant digits where necessary.

4. Continuing, we get the following table. Chapter 1 Tools Function Evaluator & Grapher to find a utility you can use to evaluate functions like this. 6 10 7 Sometimes, as in Example 4, we need to use several formulas to specify a single function. 3 One reason that more complex formulas are often less realistic than simple ones is that it is often random phenomena in the real world, rather than algebraic relationships, that cause data to fluctuate. Attempting to model these random fluctuations using algebraic formulas amounts to imposing mathematical structure where structure does not exist.

A. f (0) 2. ● a. f (−1) b. f (2) 8. ● Given g(x) = 2x 2 − x + 1, find a. g(0) b. g(−1) c. g(r) d. g(x + h) 1 9. ● Given g(s) = s 2 + , find a. g(1) b. g(−1) s c. g(4) d. g(x) e. g(s + h) f . g(s + h) − g(s) 1 10. ● Given h(r) = , find a. h(0) b. h(−3) r +4 c. h(−5) b. f (1) 3. ● a. f (2) − f (−2) b. f (−1) f (−2) 4. ● a. f (1) − f (−1) b. f (1) f (−2) c. −2 f (−1) c. 3 f (−2) 5. ● Given f (x) = 4x − 3, find a. f (−1) b. f (0) c. f (1) d. f ( y) e. f (a + b) hint [see Example 2] ● basic skills b. f (0) d.

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