A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- + -...) 6 1² 2² 3² x(π-x) = = +

Q: 10. Since (7,-1) is a point on f (x) cos z,which point will be found onf'(x) = cosx ? %3D O a (1,ח)…

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Q: 4x 16. 6x 7. 2y 17. 3y2

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Q: Given So (x) = exp{- (Ax + Bx² + D* – } In D Calculate |10930 ƒor t = 10 round to 4 decimal places…

A: t|10q30 is the probability that a life aged 30 years will survive the next t years and will die…

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

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Q: 2#), 3. What are the first three terms of the series n=1 ? A. 2 4 6 x3 В. 2 4 6 + x4 x² x6 c. 2 4 6…

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Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

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Q: f (x) = cos(2\x) Find the MacLaurin Series for = Cos(2.

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Q: The first derivative of the power series 9 9x2 9x3 9x4 f(x)=9+ .. is 1! 2! 3! 4! O -9 f(x) O f(x)…

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Q: 6. For positive integer n, prove the following (given that I(½) = √√): √π = (2n)! √T. 4nn! T(n +…

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Q: 9. The Theorem of Pappus will always be applicable to determine the volume of solid revolution for…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Write the nth term ( general term) for these Maclaurin series  1) (e^x)(cosx) 2)(e^x)(sinx)

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Q: f (x) = arctan(r²)

A: We know that power series of arctan(x)

Q: 1/16 Perform a test to determine if tan (80)d0 converges. b lim tan(80)d0 b-x/ 16" 0 (Simplify your…

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Q: 5.) Scosx (69425 Jax Са (9 + 25 sin(x) dx

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Q: What is the 1st term in the power series expansion of the function y = cos x? A) x B 1 (c) о D) x^2

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Q: dy If y = 9sin x then dx (a) (cosx) 9sin x (b) (In 9)9 sin x (c) 9sin x (d) (In 9)(cosx) 9sin x

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Q: [(1-4cosec'x)d = O a. x+4 cot x + c O b. - 4 cot x+c x-4 cot x + c O d. 4 cotx+c

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Q: 1. A power series is a series of the form and cn's are where x is a 2. The power series can be…

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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: te the Taylor series for f(x) = S

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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: 13. (a) Write out the first six terms of the series COS k=1 (b) Show that this series can be…

A: Solution of given problem is followed by

Q: 4) (a) Find a deqree 3 power series for the function sin(x) centered at T fla) = f (2) + f(a) (x-a)…

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Q: dn Find a general formula for den by identifying a pattern in parts (a) through (c). To begin,…

A: We use the given details and differentiation formula to find answer

Q: 6. dx = x + 4x + 5 (A) arctan(x + 2) + C (B) arcsin (x + 2) + C (C) In|r*+ + 4x + + C 1 (D) + C x° +…

A: Proceed as shown below...

Q: 1. A power series is a series of the form and Cn's are where x is a

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 5x Represent the function as a power series f(x) = >, Cnx" 6+ x n=0 Co = C1 = C2 = C3 = C4 =

A: According to the given information, it is required to represent the function as power series.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT h¯¹ (z) = 1/2 ln (1+2) 1-z Show that tanh

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Q: (3) Let A = 6. We have shown that A" = CnA + dnI for some sequences {Cn} -3 and {dn}. Find A" for…

A: Given that A=266-3  To show that An=cnA+dnI for some sequences cn and dn A-xI=0 where x is…