The Maclaurin series for f(x)=cos(/x) Select one: x2 + 2! 4! 6! .3 O 1+ 2! 4! 6! x? x O 1 2! 4! 6! x3 O 1+ * 2! 3! x? O 1+. 2! 4! 6!

Q: Prove that the sequence {sin n + cos n is bounded. =1

A: The given sequence is We have to prove that the sequence is bounded.

Q: The Fourier series of the given piecewise function has -n < x < 0 0<x < n -3 when f(x) = { 3 %3D…

A: The solution is given as

Q: If a function is of the type y = A sin(B(x - C)) - DMath output error and the amplitude is 3, there…

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Q: Prove & [a+(i-1)d] =na + dn(n-1) where a and d are fixed real numbers. 2 n Use the properties of…

A: To prove :- ∑i=1na+i-1d=na+dnn-12

Q: 4) Define f: N→R as follows: f(1) = 3, f(2) = and for n > 3 f(n) = f(n- 1) + f(n- 2) %3D 2' Prove…

A: Consider the provided question, According to you we have to solve only question no. (4). (4) Given,…

Q: Use mathematical induction to prove the following statement derivatives of the function f(x) = x¯¹…

A: We have to prove that the nth derivative of  where  is using mathematical induction

Q: Using the binomial expansion n (1 + x)² = ± (1) x², k=0 prove the following relations n n…

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Q: Q3. Use the Maclaurin expansion of er and the definitions sinh x = (e* – e-*)/2 and cosh x = (et +…

A: To show: a) sinhx=x+x33!+x55!+....                b) coshx=1+x22!+x44!+.... Concepts used: 1.…

Q: Evaluate f x(x- 1) dx | c. (x + 1) -x + 1) +C D.x – 1) -- 1) +c x(3 35 1)z (x- | | 35 35 35 |

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Q: Assume that the coefficients in the expansion f(x) = anx" n=0 satisfy Enanx" – E Anx"+1 = 0. n=1 n=0…

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Q: (a) Let the interval a, b be divided into n equal sub-intervals such that a = x0 < a1 < x2 < x3…

A: From this general formula we can obtain different integration formulae by putting n=1, 2,3 etc. We…

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

Q: Given: sinx = (-1)" (2п+1)! x2п+1for x € R n=0 Compute the exact value of the sum 0-1)"(2n+1) „2n+…

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Q: x[n]=(0,7)n.u[n] and h[n]=(0,9)n.u[n] to be y[n]=x[n]*h[n] Get the result of my processing…

A: Solution is in step 2

Q: 13. (a) Express each of following sum in sigma notation 1 a) 1 + 2 + 113 +... + 1 20 b)…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Suppose r1,r2, . . . is a sequence that contains every rational number. Let 1 1 F = R \U (rk 2k k=1…

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Q: Using Sandwich Theorem, the sequence 2 an = 4 – Cos n2 + 1 - O diverges O converges to 4 converges…

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Q: 7. Prove by induction. For any n2 0, E F = F,Fn+1• k=0

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Q: Calculate the limits by arguing with the power series representations of each function. Tipp: 4 =…

A: We can expand each function into its corresponding power series and then assess the limit by looking…

Q: Let f(x) = 1 - 2x where 1 0 ≤ x ≤ Expand f(x) to a 4 Fourier sine series converging to 1 f(x) on the…

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Q: Prove that 1 (c) 2F₁ (a, b; c; z)

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Q: Determine the limit of the sequences (2 * n + 1)2 – (n – 1)2 an = (n + 1)2 – (n – 1)2 cos(42 * n3)…

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Q: Q3) Express cos(x²) as a power series. а) 1. 2! + 6! 4! x10 + 3! x14 +. 7! b) 1– 5! c) 1– x5 x7 + 7!…

A: To express the function cos(x2) as a power series. Here, note that the power series of the function…

Q: Q3) a) Evaluate x-23(3x) dr. b) Expand the following function in a Fourier Bessel series using…

A: a) Evaluating the integral  This integral can be solved using integration by parts. Choose the…

Q: 2)Given 1 0<x <5 f (x) = 1 1 <x <1 2 Find b) the Fourier sine series expansion of f (x) 3 cos3nx…

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Q: 3. 6, Giraph of g'(x) Let fbe the function given by f(x) = (In x)(sin x). The figure below shows the…

A: For gx to be a increasing function, its derivative g'x must be greater than zero. From the given…

Q: Consider the function fa: [1,2)R defined by : fa(2) = 6- 2r. The expression of the upper sums, S,…

A: Given function is f2:1,2→ℝ where f2x defined by  f2x=6-2x                     (i) To find the…

Q: 6) E(-1y " Ans. Diverges, a,1 n+1

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Q: Prove that these two E E cos (Tin) não Inn 2 are تم 22=1 convergent (-1) h 22²41

A: A series is defined as the combination of the sequence. A series is said to be convergent when n…

Q: Prove by induction on n, that for all real x € R with sin(x) ‡0 we have sin(2nx) cos(x) + cos(3x) +…

A: We need to prove by induction on , that for all real  with , the following result holds..We know…

Q: The expansion 1 + x + x² ... approximates (1 - x)1 if O x is not equal to 1 本 O absolute value of x…

A: The expansion 1+x+x2+.........approximtes 1-x-1

Q: Cos 720 n! + A) diverges B) converges

A: if sum of series is finite then series is convergent. so we need to find sum of the series. note…

Q: 5. Prove that . Hint: Compute e-' from the continued frac e - 1 1 + 2 + 3 + ·…. tion for et given in…

A: When a series is in the form ∑k=1∞-1k-1α1α2α3...αk, we can express it as a continued fraction as…