In Exercises 1–28, compute the products. Some of these may be undefined. Exercises marked should be done by using technology. The others should be done in two ways: by hand and by using technology where possible. [HINT: See Example 3.]
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Finite Mathematics
- For the functions in Exercises 39–42,arrow_forwardIn Exercises 31–36, find a general formula for f®)(x).arrow_forwardClassify the quadratic forms in Exercises 9–18. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. 11. 2x² + 10x1x2 + 2x3arrow_forward
- Scientific Notation. In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation. 614arrow_forwardIn Exercises 11–14, use a product-to-sum formula to find the exact value. (See Example 2)arrow_forwardIn Exercises 19–22, show there is a number c, with 0 ≤ c ≤ 1, such that f(c) = 0. 19. F(x) = x3 +x3− 1arrow_forward
- In Exercises 31–38, find the absolute maxima and minima of the func-tions on the given domains.arrow_forwardIn Problems 31–34, find the complex zeros of each polynomial function f1x). Write f in factored form.arrow_forwardIn Exercises 83–92, factor by introducing an appropriate substitution. 83. 2r* – x? – 3 84. 5x4 + 2x2 3 85. 2r6 + 11x³ + 15 86. 2x + 13x3 + 15 87. 2y10 + 7y + 3 88. 5y10 + 29y – 42 89. 5(x + 1)2 + 12(x + 1) + 7 (Let u = x + 1.) 90. 3(x + 1) - 5(x + 1) + 2 (Let u = x + 1.) 91. 2(x – 3) – 5(x – 3) – 7 92. 3(x – 2) – 5(x – 2) – 2arrow_forward
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