2. Find series representations for the following functions: (a) f(x) = 1 (b) f(x) = 27 1+x4 1+ 4x2 (c) f(x) = 5x3 –- 13x2 +7 CO (-ズ) n= 0 52-(3x+ ) neo

Calculus: Early Transcendentals
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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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Please answer question 3
HW 13,14
Josaph mikuancar
13
GROUP WORK, SECTION 11.9
Find the Series
g* = 1+x+x² + x³ + . ...
It has been said, both in class and in the text, that
1-x
1. This statement seems to have some problems with it. For example, if x = 2, it is clearly false that
1-2
= 1+2+4+ 8+ 16+.... What do your instructor and textbook author mean when they say
=1+x+x² + x³ + ...? (1+ x)" =Itnx+ n(n-1) ,2
1-x
nin-l)(n-2)3.
20
31
so bihom al
((-x) = 1+ (-1)(-)+ (-)(-1-)
メ=2 >」
capan. fails
31
2. Find series representations for the following functions:
(b) f(x)=1+ 4x²
27
(a) f(x) =
(c) f(x) = 5x³ – 13x² + 7
CO
1-つ
(-ズ)
5,-(3-+ 7)
n=0
neo
r= 5x3-132 t6
5x3-13,2 +7
Co
(52-13-と
Sy513,2+7
x - 5x2 + 6x
x- 2
(d) f(x) = In|1+x³|
(e) f(x) = + 2x³ – x
1-x4
(f) f(x) =
I-r=-x4
x + 2x²_2x=-x5
r=2x7_x5+x9-2-1
「-r メ-2
x² 5? +6x
「= x5ん?+コx+z
Inlitx1
2xーx5ー2x
In litx31
CO
(ト。
xP-5+6x,
2x-ド-2パ
678
O 2012 Cengage Learning. All Rights Resorved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Transcribed Image Text:HW 13,14 Josaph mikuancar 13 GROUP WORK, SECTION 11.9 Find the Series g* = 1+x+x² + x³ + . ... It has been said, both in class and in the text, that 1-x 1. This statement seems to have some problems with it. For example, if x = 2, it is clearly false that 1-2 = 1+2+4+ 8+ 16+.... What do your instructor and textbook author mean when they say =1+x+x² + x³ + ...? (1+ x)" =Itnx+ n(n-1) ,2 1-x nin-l)(n-2)3. 20 31 so bihom al ((-x) = 1+ (-1)(-)+ (-)(-1-) メ=2 >」 capan. fails 31 2. Find series representations for the following functions: (b) f(x)=1+ 4x² 27 (a) f(x) = (c) f(x) = 5x³ – 13x² + 7 CO 1-つ (-ズ) 5,-(3-+ 7) n=0 neo r= 5x3-132 t6 5x3-13,2 +7 Co (52-13-と Sy513,2+7 x - 5x2 + 6x x- 2 (d) f(x) = In|1+x³| (e) f(x) = + 2x³ – x 1-x4 (f) f(x) = I-r=-x4 x + 2x²_2x=-x5 r=2x7_x5+x9-2-1 「-r メ-2 x² 5? +6x 「= x5ん?+コx+z Inlitx1 2xーx5ー2x In litx31 CO (ト。 xP-5+6x, 2x-ド-2パ 678 O 2012 Cengage Learning. All Rights Resorved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1/144
10
222/143
1 1
223
Find the Series
3. Find the radius of convergence for each of the series you found in Problem 2.
brit
4. Find an approximate value for In |1+x'| dx.
Transcribed Image Text:1/144 10 222/143 1 1 223 Find the Series 3. Find the radius of convergence for each of the series you found in Problem 2. brit 4. Find an approximate value for In |1+x'| dx.
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