1 Limits And Continuity 2 The Derivative 3 Topics In Differentiation 4 The Derivative In Graphing And Applications 5 Integration 6 Applications Of The Definite Integral In Geometry, Science, And Engineering 7 Principles Of Integral Evaluation 8 Mathematical Modeling With Differential Equations 9 Infinite Series 10 Parametric And Polar Curves; Conic Sections 11 Three-dimensional Space; Vectors 12 Vector-valued Functions 13 Partial Derivatives 14 Multiple Integrals 15 Topics In Vector Calculus expand_more
9.1 Sequences 9.2 Monotone Sequences 9.3 Infinite Series 9.4 Convergence Tests 9.5 The Comparison, Ratio, And Root Tests 9.6 Alternating Series; Absolute And Conditional Convergence 9.7 Maclaurin And Taylor Polynomials 9.8 Maclaurin And Taylor Series; Power Series 9.9 Convergence Of Taylor Series 9.10 Differentiating And Integrating Power Series; Modeling With Taylor Series Chapter Questions expand_more
Problem 1QCE: What characterizes an alternating series? Problem 2QCE: (a) The series k=11k+1k2 converges by the alternating series test since and . (b) If... Problem 3QCE: Classify each sequence as conditionally convergent, absolutely convergent, or divergent.... Problem 4QCE: Given that limk+k+14/4k+1k4/4k=limk+1+1k44=14 is the series k=11kk4/4k conditionally convergent,... Problem 1ES Problem 2ES Problem 3ES: Determine whether the alternating series converges; justify your answer. k=11k+1k+13k+1 Problem 4ES Problem 5ES Problem 6ES: Determine whether the alternating series converges; justify your answer. k=31klnkk Problem 7ES: Use the ratio test for absolute convergence (Theorem 9.6.5) to determine whether the series... Problem 8ES Problem 9ES: Use the ratio test for absolute convergence (Theorem 9.6.5) to determine whether the series... Problem 10ES Problem 11ES: Use the ratio test for absolute convergence (Theorem 9.6.5) to determine whether the series... Problem 12ES: Use the ratio test for absolute convergence (Theorem 9.6.5) to determine whether the series... Problem 13ES: Classify each series as absolutely convergent, conditionally convergent, or divergent. k=11k+13k Problem 14ES: Classify each series as absolutely convergent, conditionally convergent, or divergent.
Problem 15ES Problem 16ES: Classify each series as absolutely convergent, conditionally convergent, or divergent. k=11k+1k! Problem 17ES Problem 18ES Problem 19ES: Classify each series as absolutely convergent, conditionally convergent, or divergent.... Problem 20ES Problem 21ES: Classify each series as absolutely convergent, conditionally convergent, or divergent. k=1sink2 Problem 22ES Problem 23ES: Classify each series as absolutely convergent, conditionally convergent, or divergent. k=21kklnk Problem 24ES: Classify each series as absolutely convergent, conditionally convergent, or divergent. k=11kkk+1 Problem 25ES: Classify each series as absolutely convergent, conditionally convergent, or divergent. k=21lnkk Problem 26ES Problem 27ES: Classify each series as absolutely convergent, conditionally convergent, or divergent. k=11k+1k!2k1! Problem 28ES Problem 29ES: Determine whether the statement is true or false. Explain your answer. An alternating series is one... Problem 30ES: Determine whether the statement is true or false. Explain your answer. If a series satisfies the... Problem 31ES: Determine whether the statement is true or false. Explain your answer. If a series converges, then... Problem 32ES: Determine whether the statement is true or false. Explain your answer. If uk2 converges, then uk... Problem 33ES: Each series satisfies the hypotheses of the alternating series test. For the stated value of n, find... Problem 34ES Problem 35ES: Each series satisfies the hypotheses of the alternating series test. For the stated value of n, find... Problem 36ES: Each series satisfies the hypotheses of the alternating series test. For the stated value of n, find... Problem 37ES: Each series satisfies the hypotheses of the alternating series test. Find a value of n for which the... Problem 38ES Problem 39ES Problem 40ES: Each series satisfies the hypotheses of the alternating series test. Find a value of n for which the... Problem 41ES: Find an upper bound on the absolute error that results if s10 is used to approximate the sum of the... Problem 42ES Problem 43ES Problem 44ES Problem 45ES: Each series satisfies the hypotheses of the alternating series test. Approximate the sum of the... Problem 46ES Problem 47ES: The purpose of this exercise is to show that the error bound in part (b) of Theorem 9.6.2 can be... Problem 48ES: Prove: If a series ak converges absolutely, then the series ak2 converges. Problem 49ES: (a) Find examples to show that if ak converges, then ak2 may diverge or converge. (b) Find examples... Problem 50ES: Let uk be a series and define series pk and qk so that pk=0,uk,uk0uk0andqk=uk,0,uk0uk0 (a) Show that... Problem 51ES Problem 52ES Problem 53ES: Exercise 51 illustrates that one of the nuances of “conditional� convergence is that the sum of... Problem 54ES: Exercise 51 illustrates that one of the nuances of “conditional� convergence is that the sum of... Problem 55ES: Exercise 51 illustrates that one of the nuances of “conditional� convergence is that the sum of... Problem 56ES: Consider the series 112+2313+2414+2515+ Determine whether this series converges and use this series... Problem 57ES format_list_bulleted