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Q6. (1) Given log(1+t) = t = t + t² 4 valid for 1411, determine the power. series for log (1+2x) up to powers of and write down the radius of convergence, t 2 3 11/ Given e² = 1+t+t² +² +-n, valid for all t t 2! 3! 2 = 1+t+t²rt³ron, valid for 161 <1, 3 and 1-t 3 Show 2* = 1-2x + x²-12 X² + --- 17 4 24 1 + 2/1/2012

Q6. (1) Given log(1+t) = t = t + t² 4 valid for 1411, determine the power. series for log (1+2x) up to powers of and write down the radius of convergence, t 2 3 11/ Given e² = 1+t+t² +² +-n, valid for all t t 2! 3! 2 = 1+t+t²rt³ron, valid for 161 <1, 3 and 1-t 3 Show 2* = 1-2x + x²-12 X² + --- 17 4 24 1 + 2/1/2012

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.4: Logarithmic Functions
Problem 7E
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Q6. (1) Given log (1+t) = t-t² +t²-t ² + --- 2 3 4 valid for It<l, determine the power. series for log (1+2x) up to powers of and write down the radius of convergence, e² = 1+t+t² +t² + --, Valid for all t 4 t 2 3 11/ Given 2! 3! 1+t+t+t²³ton, valid for IE) <1, × and 1-t show * = 1-3x + 5 2 1+%22 3 3 4-5X²³-12x²³ +²² x² 4
Transcribed Image Text:Q6. (1) Given log (1+t) = t-t² +t²-t ² + --- 2 3 4 valid for It<l, determine the power. series for log (1+2x) up to powers of and write down the radius of convergence, e² = 1+t+t² +t² + --, Valid for all t 4 t 2 3 11/ Given 2! 3! 1+t+t+t²³ton, valid for IE) <1, × and 1-t show * = 1-3x + 5 2 1+%22 3 3 4-5X²³-12x²³ +²² x² 4
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