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: Q5: a\. Let f(x) = x³ - 3x² -1, x ≥ 2. State and prove the theorem of derivative of inverse…

A: Here , f(x) = x3-3x2-1 We find required value.

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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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Q: Let f be a function whose Maclaurin series expansion is given below. f(x) = 3+ 12x + 24x² + 32x³ +..…

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Q: (b) Expand and simplify in ascending powers of x as far as the term in x" 1+3x

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

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Q: Find a Taylor series expansion around x = 2 for f(x) = ln x

A: To find the Taylor series expansion for f(x)=ln(x) around x=2 is given by :-

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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: Find the power series expansion of / 1 + x Sin 2 x.

A: Given the function 1+x sin2x. Let f(x)=1+x sin2x. Now let take g(x)=1+x and h(x)=sin2x.

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Q: A) The fraction  b/a  may be written as  b/a = (a+b−a) / a = 1 + (( b−a ) / a ). Use the power…

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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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