Question 6. Use Maclaurins theorem to calculate the series expansion of f(x) including the term in x'. = tan x up to and [a] x-x+ - fr' +0(x*) [b] t +0(x*) [e] not in the list [c] 1+r?+O(x*) [d] x-+0(x*)

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Q: 5. Expand f(z)=2/((z+1)(z+3)) in a Laurent series valid for (a) 1<|z|<3, (b) 3<|z], (c) 0<|z+1|<2,…

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Q: Suppose x cannot = 1. Use induction on n to prove the following formula is true for all integers n…

A: We will prove the given statement.

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A: Since z&gt;1 then 1z&lt;1, Now, we write the function f(z)=ln11-z      =ln1-z1-1z…

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A: A Macluarin series is a Taylor series expansion 0 a function about 0…

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A: It is given that the domain is z&gt;1, then 1z&lt;1. Consider the given function fz=ln11-z.…

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Q: 12. Find a Taylor series representation for the function f(x) = sin(x) about a = 2 (a) 1 - (x-7² 2!…

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Q: 6. If f(x) = then the Maclaurine series for f(x) is ++3x a) c) Ž3x) b) E-D* 3* x* d) Ž(-1)" x*

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A: The given series is summation of (-1)n+1/(n3+1), n from 2 to infinity.

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Q: 24. Let f be a function such that f'(x) Maclaurin series for f? = sin 9 (A) x - + 10 216 9 X (B) 2x…

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Q: A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- 6 +…

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Q: Find the Taylor series for B Σ (-1)" ΟΣ (x-1)^ n=0 2" (-1)" #=0 2"+1 1 x+1 ΟΣ ΟΣ © Σ+(x-1) " at x =…

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Q: Show that as a half range series of cosine terms for 0 < x < 1, /cos 2x cos 4x cos 6x + 12 2² 3²…

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