=E512( 6, (-1)º-k(x)18–6k 18-6k k=0

Q: Find the first five terms of the Taylor series for the function f(x) = ln(x) about a=2. (Your…

A: Taylor series of any function f(x) centered at x=a, is given by: ∑n=0∞f(n)(a)n!(x-a)n

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

A:

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: Given, x1/2+y1/28 where n=8 total number of terms =8+1=9 middle term =n2+1 82+1=5 5th term is a…

Q: Find L-1. by convolutions. l(s-1)².

A:

Q: 23. Using mathematical induction, show that dn n [F (x) · g(x)] = D dk [f(x}] • n dn-k dxn k) dxk…

A:

Q: bility 0.2. Supposing that there are only sunny or rainy days, in the long run on what fraction of…

A: here given ,  On a Southern Pacific island, a sunny day is followed by another sunny day with…

Q: Show that kT| e-t²/kTdt = (kT)3/2 " 0. 2

A:

Q: sion By A knawn x²-5x_x+5 ーちメメ -X cr ar

A:

Q: 62. a. Show that e>1+x for x > 0.

A: We will answer the first question only as those all are different and we don't answer multiple…

Q: 1 ER=1 (- 100 k%3D1 2k+1

A:

Q: ntiderivative. 7x x² -x-2 OB. In x + 1|-In x- 2| + c 14 .7 14 In x +1- x +1 In x-2 x- 2 3 3 14 7 OD.…

A:

Q: (3) Let X = n(µ,4) and Var(2x) = E(4-7x) find u.

A: Given,X~n(μ , 4)

Q: 67. Find a reduction formula for e- dx

A: Given that ∫xne-xdx find the reduction formula

Q: 2. Find the odd and even half range expansion- f(t) 2 2

A: The given problem is to find the Fourier odd half range expansion and Fourier even half range…

Q: Calculate the residue of eZ.e-5=0

A:

Q: (Зп+5 Find infimum of A |n E N} n+9

A:

Q: = x3 + x - rith starting d with the of x after the

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Q: nson meth x-1 = 0. I

A:

Q: 33. (a) L²₁ let - 11 dx r3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: et H={Φ∈Sn | Φ(n)=n}. Find index of H in Sn.

A: H=ϕ|ϕ(n)=n=I (group of identity permutation)o(H)=1o(Sn)=n!index of H in Sn=n!1=n!

Q: 1) E k=1 4-

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

A:

Q: 2n²+3n 2 3) Prove (with an e - N proof): lim n-0o 3n2+8n+2 3

A:

Q: (b) Use the iteration formula 4(3-х,) (3+x,) with x, = 1 to find, to 2 decimal places, the value of…

A:

Q: 2. Define Ej where the reactor rise time of the first batch is less than 55 min. and E2 where the…

A: Given: E1=The reactor rise time of the first batch (t<55)E2=The reactor rise time of the second…

Q: 83 Expand log (cer) Theosem in poue og (x-2) wing Taylor's

A:

Q: Calculate the residue of eZ.e-5=0

A:

Q: Show that 100 1 arctan(100) – arctan(2) + E s arctan(100) – arctan(2) + 1+ 1002 1+ k2 k=2 1+ 22

A: To show that: arctan100−arctan2+11002≤∑k=210011+k2≤arctan100−arctan2+122

Q: 16. There is a very quick way to compute £-, 2'(-1)ª-' (); do use it. l=D0

A: Introduction: The binomial theorem is very important in mathematics. For any real numbers a,b with…

Q: 4. Prove the formula below using mathematical induction log 2k u + zu log 2 k=1

A: Given: Formula: ∑k=1n log2k=n2+n2log2

Q: 5n2 For E>0, there is a corresponding N such that -4/0 N. 4 +3 Then the value of L will be

A: Given function is , f(n)=5n24n+3

Q: he sales of Universal Systems in the 1st t years are given by:S(t) = tv0.2t + 4 where S(t) is in…

A: Given query is to find the average sales for 1 to 10 years .

Q: Q1 In the expansion of a(2+ax) 11 He Co-efficient ef te term in i8 11880. Find te value of a .

A:

Q: Calculate the residue of e.e5=0

A:

Q: 2と e こeo437 RK = k(-n.65)

A: To solve this problem, first we should bring all the terms with k to one side of the equation and…

Q: az Find for z = e2z-y.

A: Given : z = e2x - y

Q: 4. Prove the formula below using mathematical induction n nº + n log 2* : ") log 2 2 k=1

A: Use mathematical induction to prove the given equation. Let n=1LHS:log 21=log 2RHS:1+12log 2=log…

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…

Q: 1 Integrate

A:

Q: x is within 5 units of 1. Olx-1 s5 |x - 1|> 5 |x -1|2 5 Olx-11-5

A: We will solve the problem

Q: 3. A ceramic insulator is baked at 400o C and cooled in a room in which the temperature is 25º C.…

A: Follow the procedure given below.

Q: Apply Heaviside's expansion formula to 3s +1 (s− 1)(s²+1)

A: Here we have to find the Laplace inverse of 3s+1(s-1)(s2+1) i.e. L-1[3s+1(s-1)(s2+1)] by applying…

Q: k Ink is Ln=1 (k+1)3 In k а. k2 In k+ln 1 b. k3 In k+ln 1 с. k2 In k d. k3

A: Serie and sequence, limit comparison test

Q: h[n] = -8[n +1] + 8[n] + 28[n- 1] * x[n] = 8[n+ 1] + 28[n] + 8[n- 1] %3D - Find output vlnl = x[n] +…

A: Please find step by step solution below:

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: 7. E(-1)"- Vn +1 n=1

A:

Q: 3RD ITERATION: x₂ = 3-X₂ +2₂ 3-1 + 1.1875 = 1.0625 3 3 Yo= 7-2x₂₁-22-7-2 10.757-1-1875 4 4 1.078125…

A:

Q: sin(2x³) x² 11. Approximate justify your result. within 0.0001 if x = 1/3 using its Mac expansion…

A: Solution: Given function is, f(x)=sin2x3x2 sin(x)=∑n=0∞-1nx2n+12n+1! f(x)=∑n=0∞-1n2x32n+12n+1! x2…

Q: 6) Use the first three terms of the Taylor expansion for f(x) = cos(x) to estimate cos(1/8). %3D

A: We have to find the value of cos(1/8)using only first three terms of Taylor's series.

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.