a) Evaluate the given integral x + 3x – 3 (x + 1)(x² + 6x + 10) b) sin'x cosx+sinx c) Find the Mclaurin series for the function an up to 5 terms tanx

Q: Which of the following information is correct for the sequence 3 7 dx 1 dx 1 dx dx {an}n=l X (a) The…

A: Given: The given sequence is ann=1∞=13∫13dxx,15∫15dxx,17∫17dxx,19∫19dxx.....

Q: Determine the number of terms necessary to approximate cos x to 8 significant figures using the…

A: We have to determine the number of terms necessary to approximate cosx to 8 significant figures…

Q: Relate the well-known power series from Calculus I, e* = E and the п! n=0 power series for sin x and…

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Q: 4. Find (a) the Fourier cosine series, (b) the Fourier sine series. Sketch f(x) and its two periodic…

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Q: a.) Use long division to derive the first four non zero terms of the Maclaurin series for f(x)= tanx…

A: Solution a: Since we know  tanx=sinxcosx By Maclaurin series…

Q: Find the series for cos⁡x/(1+sin⁡x ) by differentiating the power series of ln⁡(1+sin⁡x ). With…

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Q: Find the Fourier sine series for f(x) = on 2)=7 On - -L≤ x ≤L.

A: f(x) = x on –L ≤ x ≤ LFind the Fourier sine series for f(x).

Q: 2. Find the sum of the series sin?a + sin2(a + B) + sin2( a + 2B) + + sin?(a + n - 1)B ......

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Q: 1. Find the FOURIER SINE SERIES of f(x) = 2x² in the interval 0 ≤ x < .

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Q1) Find Fourier Series for the following function: - 2 <t<2 2 <t<6 a) x(t) Period ( T=8s) by using…

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Q: B- Use power series to evaluate the integral sin.x X -dx

A: We want to find integral of sinx/x using power series.

Q: Siven the following: 00 5(-1)"x2n '(-1)"x²n cos(x) = for all x E R (2n)! n=0 ) Find a power series…

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Q: Find the Fourier series of period 2n for the function scos x – sin x, -n<x< 0 lcosx + sin x, f(x) =…

A: Sketch the graph of given function.

Q: 1. Using Taylor's theorem you can approximate different functions aroimd a ceT- tain point, as you…

A: Formula of Maclaurin series of f(x) about x=a isf(x)=∑k=0∞fk(a)k!xk(a) Consider f(x)=cos θthen…

Q: Find the coefficients of the Fourier cosine series for f(x).

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Q: Evaluate lim-[(sinx-x)/x³] by u

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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.

Q: 20. Using = 00 1-x n=0 a) Find a power series for c) Find a power series for 1 1+x¹ - 4x³ (1+x¹) ²…

A: The given problem is to find the power series of the given functions with using the given power…

Q: Let f be the function defined for - ≤ x ≤ π by 1 0 f(x) if - π/2 ≤ x ≤ π/2 otherwise and then…

A: given function f defined for -π≤x≤π by fx=1if -π2≤x≤π20otherwise and then extended to be 2π periodic…

Q: Civen that the Maclurin Series f Cosine function is (17) in (-1) C 2n e Let f lx) = x cos(x?).Find…

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Q: 4 sinx+=sin3x +=sin5x+..... and that when x=, 1 1 6. If it is given that the Fourier Series is f(x)=…

A: The Fourier Series is

Q: 1) Solve for y" + (cos x)y = 0, given that cos x can be represented 1 2! + + 4! as a series of .…

A: Solution : Given, y"+cos(x)y=0 Let the expanded form of y as, y=∑n=0∞Cnxn By differentiating…

Q: Find the Maclaurin series for r2 + tan a and using that series, derive the Maclaurin series for 2x+…

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Q: Which of the following information is correct for the sequence 7. 9. dx 1 dx 1 dx 1 dx {an}n=l 5 (a)…

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Q: Determine the Fourier series for the function defined by: -1, -n < x < -· 2 π f(x) = { 1, < x <• -1,…

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