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6. As discussed in class, functions have different power series because their coefficients differ. (a) For the simple function, y = 3x + 5, what is the value of co? c1? c₂? f(n) (0) n! (b) Using the formula c₁ = - find the first six coefficients in the series for f(x) = e²* . (c) Write the first six terms in the series for f(x) = e²x. (d) Find a compact formula cn for and write the entire series for f(x) = ²x.

6. As discussed in class, functions have different power series because their coefficients differ. (a) For the simple function, y = 3x + 5, what is the value of co? c1? c₂? f(n) (0) n! (b) Using the formula c₁ = - find the first six coefficients in the series for f(x) = e²* . (c) Write the first six terms in the series for f(x) = e²x. (d) Find a compact formula cn for and write the entire series for f(x) = ²x.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. As discussed in class, functions have different power series because their coefficients differ. (a) For the simple function, y = 3x + 5, what is the value of co? c1? c₂? f(") (0) n! (b) Using the formula c,₁ = - find the first six coefficients in the series for f(x) = e²* . (c) Write the first six terms in the series for f(x) = e²x. (d) Find a compact formula cn for and write the entire series for f(x) = ²x K
Transcribed Image Text:6. As discussed in class, functions have different power series because their coefficients differ. (a) For the simple function, y = 3x + 5, what is the value of co? c1? c₂? f(") (0) n! (b) Using the formula c,₁ = - find the first six coefficients in the series for f(x) = e²* . (c) Write the first six terms in the series for f(x) = e²x. (d) Find a compact formula cn for and write the entire series for f(x) = ²x K
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