Let f :R\{-2} →R be the function given by f(z) = 2+1 a) Find the Taylor series expansion of f at zo = 1, including it's radius of convergence. Hint: It might help if you find a, b and c such that z = a(x – 1)? + 6(x – 1) +c. b) What is the value of the 213-th derivative of f at the point ro = 1?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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5. Let f : R\{-2} →R be the function given by
f(2) =
2+x
a) Find the Taylor series expansion of f at ro = 1, including it's radius of convergence.
Hint: It might help if you find a, b and e such that a? = a(x – 1)? + b(x – 1) + c.
b) What is the value of the 213-th derivative of f at the point ro = 1?
c) How many terms in the Taylor expansion of f(r) = e2" at ro = 0, are needed to estimate
the value f(-1/2) = e- with an accuracy of 5 decimal places?
Transcribed Image Text:5. Let f : R\{-2} →R be the function given by f(2) = 2+x a) Find the Taylor series expansion of f at ro = 1, including it's radius of convergence. Hint: It might help if you find a, b and e such that a? = a(x – 1)? + b(x – 1) + c. b) What is the value of the 213-th derivative of f at the point ro = 1? c) How many terms in the Taylor expansion of f(r) = e2" at ro = 0, are needed to estimate the value f(-1/2) = e- with an accuracy of 5 decimal places?
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