A Preview of Calculus: The Limit, Derivative, and Integral

Chapter 14, Problem 9

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A Preview of Calculus: The Limit, Derivative, and Integral of a Function 'Are You Prepared?' Answers 1. A = lw 2. 24 CHAPTER REVIEW Things to Know Limit (p. 872) limx Sc f 1x 2 = N As x gets closer to c, x c, the value of f gets closer to N. Limit formulas (p. 877) lim x Sc b = b The limit of a constant is the constant. lim x Sc x = c The limit of x as x approaches c is c. Limit properties (pp. 878, 880, 881) limxSc 3f1x2 + g1x2 4 = lim xSc f1x2 + lim xSc g1x2 The limit of a sum equals the sum of the limits. limxSc 3f1x2 - g1x2 4 = lim xSc f1x2 - lim xSc g1x2 The limit of a difference equals the difference of the limits. (c) Partition 30, 64 into three subintervals of equal length and choose u as the right endpoint of each subinterval. (d) Partition 30, 64 into six subintervals of equal length and choose u as the left endpoint of each subinterval. (e) Partition 30, 64 into six subintervals of equal length and choose u as the right endpoint of each subinterval. (f) What is the actual area A?