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Unformatted text preview: Home > My Assignments > Section 8.7 (Homework) About this Assignment SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University Due: Tuesday, November 29, 2005 11:06 PM EST Description Taylor and Maclaurin Current Score: 7.75 out of 20.75 Series Question Score pts 1 0/1 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 5 0.25/0.25 6 0.25/0.25 7 0.25/0.25 8 0.25/0.25 9 0.25/0.25 2/3 Viewing: Last Response View: All Responses Notes subs 3/20 4/20 3/20 3/20 2/20 3/20 2/20 3/20 2/20 1. [SCalcCC2 8.7.04.] Find the Maclaurin series for f(x) using the definition of a Maclaurin series. (Assume that f has a power series expansion. Do not show that Rn(x) 0.) Also find the associated radius of convergence. (To enter - or , type -INFINITY or INFINITY.) f(x) = sin 2x R=1 [INFINITY] Give the series using the form below. A = -1 B=2 C=2 D=1 E=2 F=1 G=2 H=1 [-1] [2] [2] [1] [2] [1] [2] [1] pts subs 1 0/3 1/20 0/3 Viewing: Last Response View: 2. [SCalcCC2 8.7.08.] Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn(x) 0.) f(x) = x3, a = -1 f(x) = 0 [-1 + 3*(x+1) - 3*(x+1)^2 + (x+1)^3] All Responses Notes pts 1 0/1 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 0.75/1.75 Viewing: Last Response View: All Responses Notes subs 3/20 1/20 4/20 3/20 3. [SCalcCC2 8.7.18.] Use a Maclaurin series derived in this section to obtain the Maclaurin series for the given function. (To enter or , type -INFINITY or INFINITY.) f(x) = e-x/2 R = -2 [INFINITY] Give the series using the form below. pts 1 0/1 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 5 0.25/0.25 6 0.25/0.25 7 0.25/0.25 1.5/2.5 subs 1/20 1/20 4/20 3/20 2/20 16/20 7/20 A = 0 [0] B = -1 [-1] C = 2 [2] 4. [SCalcCC2 8.7.20.] Use a Maclaurin series derived in this section to obtain the Maclaurin series for the given function. (To enter or , type -INFINITY or INFINITY.) f(x) = sin(x4) R=0 [INFINITY] Give the series using the form below. Viewing: Last Response View: All Responses Notes A=0 B = -1 C=2 D=1 E=8 F=4 [0] [-1] [2] [1] [8] [4] pts 1 0/1 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 5 0.25/0.25 6 0.25/0.25 7 0.25/0.25 1.5/2.5 subs 1/20 1/20 4/20 3/20 3/20 3/20 3/20 5. [SCalcCC2 8.7.22.] Use a Maclaurin series derived in this section to obtain the Maclaurin series for the given function. (To enter or , type -INFINITY or INFINITY.) f(x) = x cos(2x) R=0 [INFINITY] Give the series using the form below. Viewing: Last Response View: All Responses Notes pts 1 0.25/0.25 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 5 0.25/0.25 6 0.25/0.25 7 0.25/0.25 8 0.25/0.25 2/2 subs 1/20 4/20 3/20 2/20 3/20 2/20 3/20 2/20 A = 0 [0] B = -1 [-1] C = 2 [2] D = 2 [2] E = 2 [2] F = 2 [2] 6. [SCalcCC2 8.7.32.] Evaluate the indefinite integral as an infinite series. Give the series using the form below where K is an arbitrary constant. Viewing: Last Response View: All Responses Notes A=0 B = -1 C=2 D=1 E=2 F=1 G=2 H=1 [0] [-1] [2] [1] [2] [1] [2] [1] pts subs 1 0/2 2/20 0/2 7. [SCalcCC2 8.7.48.] Find the sum of the series. Viewing: Last Response View: All Responses Notes pts subs 1 0/2 2/20 0/2 Viewing: Last Response View: All Responses Notes pts subs 1 0/2 2/20 0/2 Viewing: Last Response View: All Responses Notes 1 [0.866] 8. [SCalcCC2 8.7.50.] Find the sum of the series. 1 [1.82] 9. [SCalcCC2 8.7.52.] Find the sum of the series. 1 [0.5] ...
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This note was uploaded on 10/21/2009 for the course MATH MA241 taught by Professor Hubbard during the Spring '09 term at N.C. Central.

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