Approximate the series of e with the finite sum M (−1)n SM(x) = Σ -(x-15)²n. 2nn! n=0 Use a graphing calculator to compare the graphs of e-(-1² with S5(x), S6(x) and S7(x) for 13 < x < (x-15)2

Q: Using the fact that f(x) = ₁¹² = Σox" for |x| < 1 represent function g(x) = 5²+1 as a power series.

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Q: Evaluate fr.co x cos(x³) dx as an infinite series.

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Q: Numerical solution of Ordinary differential equations Consider the following initial value problem…

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Q: for (b) and (c), the ending index of the sums include log. Recall lg is two-base log so lg = log_2.…

A: We have to solve the summations right from the start till the end of the number. Log properties are…

Q: If we wanted to find a power series for f(x) = (x+5)2 we could use the fact that = (x+5)2 a) First,…

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Q: Use the Taylor series for 1/ (1 - x2) to obtain a series for 2x/ (1 - x2)2.

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Q: Evaluate cos(x) – 1 + lim 2 12a4 Hint: Using power series.

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Q: (3) Give an example of a series 1 Cn that diverges even though cn < 0.0000001 for all n and limn→∞…

A: To Find: A series∑n=1∞cn for which (i)  cn&lt;10-7 for all n. (ii) limn→∞cn=0. But the series…

Q: For any positive integer n, prove that summation d divides n t(d)^(3) = ( summation d divides n t(d)…

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Q: n-1 1 series an = 256 4 Find the sum S5 of the first 5 terms of the geometric # a1 (1 - p) = n Use…

A: To find the sum  of the first five terms of the following geometric series.

Q: gence of a sequence, prove that the following statements are true. (a) lim 2n+1 5n+4 nx (b) lim 2²…

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Q: 3-x -1 <x < 3

A: 63-x &lt; 1=&gt;  63-x &lt; 1=&gt; 63-x &lt; 1=&gt; 63-x×3-x  &lt;  1×3-x                   ∵ 3-x…

Q: Find the Laurent series for function f(z) == in the regions (a) 0</2/<3. (61 3</2/<00 (C) 0</7-3/<1…

A: We have given a complex variable function f(z)=1z(z-3i) for the given conditions for z. To find the…