Explanation The function is given by f ( x ) = ln ( 1 + x ) x . Find the Taylor series of the function f ( x ) = ln ( 1 + x ) x as follows. f ( x ) = ln ( 1 + x ) x = 1 x [ ( 1 + x − 1 ) − 1 2 ( 1 + x − 1 ) 2 + 1 3 ( 1 + x − 1 ) 3 − ⋯ + ( − 1 ) n + 1 n ( 1 + x − 1 ) n + ⋯ ] = [ ( x ) x − 1 2 ( x ) 2 x + 1 3 ( x ) 3 x − ⋯ + ( − 1 ) n + 1 n ( x ) n x + ⋯ ] = [ 1 − 1 2 x + 1 3 x 2 − ⋯ + ( − 1 ) n + 1 n x n − 1 + ⋯ ] = ∑ n = 1 ∞ ( − 1 ) n + 1 x n − 1 n Thus, the Taylor series of the function f ( x ) = ln ( 1 + x ) x is ∑ n = 1 ∞ ( − 1 ) n + 1 x n − 1 n . Now find P 6 by using ∑ n = 1 ∞ ( − 1 ) n + 1 x n − 1 n

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 11.6, Problem 28E

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To approximate: The integral ∫00.5ln(1+x)xdx by using a sixth-degree Taylor polynomial.

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Chapter 11.6, Problem 27E

Chapter 11.6, Problem 29E

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1. Determine whether the following sets are subspaces of $\mathbb{R}^3$ under the operations of addition and scalar multiplication defined on $\mathbb{R}^3$. Justify your answers.(a) $W_1=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=3 a_2\right.$ and $\left.a_3=\mid a_2\right\}$(b) $W_2=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1=a_3+2\right\}$(c) $W_3=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 2 a_1-7 a_2+a_3=0\right\}$(d) $W_4=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1-4 a_2-a_3=0\right\}$(e) $W_s=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: a_1+2 a_2-3 a_3=1\right\}$(f) $W_6=\left\{\left(a_1, a_2, a_3\right) \in \mathbb{R}^3: 5 a_1^2-3 a_2^2+6 a_3^2=0\right\}$

3 Evaluate the double integral 10 y√x dy dx. First sketch the area of the integral involved, then carry out the integral in both ways, first over x and next over y, and vice versa.

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Chapter 11 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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To approximate: The integral ∫00.5ln(1+x)xdx by using a sixth-degree Taylor polynomial.

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Chapter 11 Solutions