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49. Sigma notation Evaluate the following expressions. 10 Σκ k k=1 6 b. Σ (2k + 1) k=1 4 a. C. k2 k=1 5 d. Σ(1 + n?) n=1

49. Sigma notation Evaluate the following expressions. 10 Σκ k k=1 6 b. Σ (2k + 1) k=1 4 a. C. k2 k=1 5 d. Σ(1 + n?) n=1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(Question 49 a-d and question 56)

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**Approximating Areas with a Calculator** Use a calculator and right Riemann sums to approximate the area of the given region. Present your calculations in a table showing the approximations for \( n = 10, 30, 60, \) and \( 80 \) subintervals. Make a conjecture about the limit of Riemann sums as \( n \to \infty \). **55.** The region bounded by the graph of \( f(x) = 12 - 3x^2 \) and the x-axis on the interval \([-1, 1]\). **56.** The region bounded by the graph of \( f(x) = 3x^2 + 1 \) and the x-axis on the interval \([-1, 1]\). **57.** The region bounded by the graph of \( f(x) = \frac{1 - \cos x}{2} \) and the x-axis on the interval \([-π, π]\).
Transcribed Image Text:**Approximating Areas with a Calculator** Use a calculator and right Riemann sums to approximate the area of the given region. Present your calculations in a table showing the approximations for \( n = 10, 30, 60, \) and \( 80 \) subintervals. Make a conjecture about the limit of Riemann sums as \( n \to \infty \). **55.** The region bounded by the graph of \( f(x) = 12 - 3x^2 \) and the x-axis on the interval \([-1, 1]\). **56.** The region bounded by the graph of \( f(x) = 3x^2 + 1 \) and the x-axis on the interval \([-1, 1]\). **57.** The region bounded by the graph of \( f(x) = \frac{1 - \cos x}{2} \) and the x-axis on the interval \([-π, π]\).
**49. Sigma Notation: Evaluate the following expressions.** a. \( \sum_{k=1}^{10} k \) b. \( \sum_{k=1}^{6} (2k + 1) \) c. \( \sum_{k=1}^{4} k^2 \) d. \( \sum_{n=1}^{5} (1 + n^2) \) e. \( \sum_{m=1}^{3} \frac{2m + 2}{3} \) f. \( \sum_{j=1}^{3} (3j - 4) \) g. \( \sum_{p=1}^{5} (2p + p^2) \)
Transcribed Image Text:**49. Sigma Notation: Evaluate the following expressions.** a. \( \sum_{k=1}^{10} k \) b. \( \sum_{k=1}^{6} (2k + 1) \) c. \( \sum_{k=1}^{4} k^2 \) d. \( \sum_{n=1}^{5} (1 + n^2) \) e. \( \sum_{m=1}^{3} \frac{2m + 2}{3} \) f. \( \sum_{j=1}^{3} (3j - 4) \) g. \( \sum_{p=1}^{5} (2p + p^2) \)
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