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

Q: Find the sum of the series ) sin2n 1 n=1 OA. tan? 1 OB. sec2 1 C. The series diverges OD. 1+ sin? 1…

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Q: 1 Use the identity sin²x = to obtain the Maclaurin series for sin² r. Then differentiate this series…

A: Here is the step by step solution of ques 4.

Q: What are the first three non-zero terms in the Maclaurin Series of f(x) = e* sin(x)? x - +-- О а.…

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Q: Use the identity cos^2 x = 1/2 (1 + cos 2x) to find the Maclaurin series for f (x) = cos^2 x.

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Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin²x. Hence, evaluate sin² x 0.5 1.0.5 5…

A: The given problem is to evaluate the given definite integral using Maclaurin series of sin2x upto 3…

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A: ∑n=1∞sin(4n) -------- Limit comparison Test:- Let we have two series a_n and b_n [b_n!=0]…

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Q: . (a) Find the Taylor series of cos 2x at x = 0, either by direct calculation or by using the known…

A: a) The Taylor series expansion for cosx at x=0 is, cosx=1-12!x2+14!x4-16!x6+.... Replace x by 2x in…

Q: Find the Maclaurin series of sin (a*). n=0

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Q: use the identity cos2 x = 1/ 2 (1 + cos 2x) to find the Maclaurin series for f (x) = cos2 x.

A: Given the function f(x)=cos2(x). We need to find the Maclaurin series using the identity cos2 x = 1/…

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: The Maclaurin series of g(x)=sin (x) is ?

A: Maclaurin series is given by:

Q: 1- Find &, and Ea of sin (x) for x = 2 with 1-8 terms of the series. sin(x) - Σ k-0 (-1)* (2k + 1)!…

A: Given : sinx=∑k=0∞-1k2k+1!x2k+1  =x-x33!+x55!-. . . . . . To Find : et   ,  ea Note : According to…

Q: Why the integral test doesn't apply to the series?

A: according to the integral test the function f(x) is positive, decreasing, and continuous function…

Q: 1 3. Obtain the Maclauring series for sin-' x= - t2"

A: Here we have to obtain the Maclaurin series for sin-1x=∫0x11-t2dx ....................... (1)

Q: Determine the first term of the Maclaurin series g(x)= (d/dx){sin(-x^2)}. Blank 1 6x5 10x9 ... 14x13…

A: The Taylor series of a function, f(x) about x=a is defined as f(x)=∑n=0∞f(n)(a)n!(x−a)n. The…

Q: 4. Find the first four nonzero terms in the Maclaurin series of -{7 sin z x +0 r = 0 f(æ) = { and…

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Q: 6. Integrate the following. Leave your answer as an infinite series. Sa sin (x³) dx а. b. dx

A: b. ∫01e-x2dx Given function is e-x2. Since  ex  is given as : ex=1+x+x22!+x33!+...   =…

Q: How did you get the expression for xtan-1(x)? How did you relate it with the maclaurin series of…

A: We use the Maclaurin series of tan-1x and multiply it by x on both the sides to get the Maclaurin…

Q: b, Find the sum of the series (x + 1)" n=2 and provide one of the intervals on which it converges.…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin? r. Hence, evaluate 0.5 sin² x dx. Give…

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Q: Write the first four non-zero terms of the power series for f(x) = 2x sin(x')- 4 %3D | about x = 2x…

A: We will use the power series expansion of sin(x) and then modify it to denote the given series as a…

Q: The Taylor series for sin x, cos r: sin r =

A: As you have posted two questions I'm answering first of them.You can re post the question for the…

Q: Find the Maclaurin series of f(x) = 21 cos (– x). What is the Maclaurin series of 21 cos (-x)? Σ…

A: To find Maclaurin series of 21cos-x

Q: Find the Maclaurin series of f(x) = sin(x?) А. %3D

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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: Determine the first 6 terms of the series of Maclaurin for f(x) = 3 cos4x.

A: We need to find Maclaurin series of fx=3 cos 4x Maclaurin series is given by fx=∑k=0∞ fk0k!xk We…

Q: What are the first three non-zero terms in the Maclaurin Series of f(x) = e* sin(x)? %3D x-+-- a. X…

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Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

A: Given series'

Q: write out the first few terms of the series to find a and r, and find the sum of the series. find…

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Q: Find the Maclaurin series of tan^−1 (x). Your answer should be in terms of summation notation

A: In the question it is asked to calculate Maclaurin series of tan-1(x) and also it is asked to…

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Q: The value of limx→0 ex-1-x x² by using series is о о -1 O 0.5 O 1 O -0.5 O

A: Solving the following limit problem,

Q: Obtain the an = $ sum of the series. (sin-—-sinn) W

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Q: An approximation using four terms of a series for the number x3 cos (22) dx

A: Given:      ∫01x3cosx2dx MacLaurin series is given by            fx=∑k=0∞fkak!xk In our case…

Q: Write down the first 4 nonzero terms of the Maclaurin series of cos(x).

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Q: Sin 3+2

A: Given that ∑n=0∞sin(2n-1)3n+2 Now take, an=sin(2n-1)3n+2 Since  an≤13n+2

Q: Integrate the power series In(1 +x) = (-1)"+1 term-by-term to evaluate Sin(I +x)dx.

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Q: Find the value of the series 30 Σ tan n=2 4 -1 n*-4 4n2

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Q: Find the Maclaurin series of sin(x) 28 (-1)",2n-7 (2n +1) n=0

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Q: Given the Maclaurin series for the sine function is x x x +.. 2n+1 00 sinx Σ(-1) = X -- (2n+1)! 3!…

A: Given the Maclaurin series for sine function as

Q: Find the value of the series ∑∞ n=1 (π − πcos n)/ 4^n or show that it diverge

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Q: ») Does the series S cos(n7) converges or diverges? Vn n=1

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Q: 6. Integrate the following. Leave your answer as an infinite series. S sin (x³) dx а. b. dx

A: To integrate ∫sin (x3) dx

Q: (b) Does the series cos(nt) converges or diverges? Vn n=1

A: Test the convergence of alternating series test

Q: Find the half-range cosine and sine expansion of the function f (x)=x - x, 0<x<1. Plot the sum of…

A: Given that, f(x)=x2-x,  0&lt;x&lt;1