Match each function with its power series representation. Functions: Power Series: Function 1: 2 1 f(x) = 2+ 7x Power series (29): 247 for lel < n=0 Function 2: Power series (13): g(x) = xe. El-1)" (; Power series (83): Function 3: 1 h(x) = r*e=*, E(-1)"; n+1 n=0 Power series (37): Function 4: 1 E(-1)"; p(x) = a² In(1 + x*) for |æ| < 1. 2n +1 Power series (7): 3" Function 5: n! q(x) = Vr tan¬(VT) for |x| < 1.
Match each function with its power series representation. Functions: Power Series: Function 1: 2 1 f(x) = 2+ 7x Power series (29): 247 for lel < n=0 Function 2: Power series (13): g(x) = xe. El-1)" (; Power series (83): Function 3: 1 h(x) = r*e=*, E(-1)"; n+1 n=0 Power series (37): Function 4: 1 E(-1)"; p(x) = a² In(1 + x*) for |æ| < 1. 2n +1 Power series (7): 3" Function 5: n! q(x) = Vr tan¬(VT) for |x| < 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Transcribed Image Text:Match each function with its power series representation.
Functions:
Power Series:
Function 1:
2
1
f(x) =
2+ 7x
Power series (29):
247 for lel <
n=0
Function 2:
Power series (13):
g(x) = xe.
El-1)" (;
Power series (83):
Function 3:
1
h(x) = r*e=*,
E(-1)";
n+1
n=0
Power series (37):
Function 4:
1
E(-1)";
p(x) = a² In(1 + x*) for |æ| < 1.
2n +1
Power series (7):
3"
Function 5:
n!
q(x) = Vr tan¬(VT) for |x| < 1.
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