Suppose we use a 6-th degree polynom, PeW to estimete gox) = 2e* with data points (Xi,9(X;)) where the Xi's are evenly spaced over the interval and include the endpoints of the interval. Given an upper bound on the eror 190-25)-Po(023) on [0,25]

Q: Without doing any calculations in Aut(Z105), determine how manyelements of Aut(Z105) have order 6.

A: Given: Automorphism, AutZ105To find: Number of elements of AutZ105 having order 6.

Q: Which of [0], [1], [2], [3], [4] is equal to [3]^2023 in Z_5? What is [15]^1989 congruent to in…

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Q: need to use L'nopitals indteterminate X2+3x+2 Why do we ile an to find limit such as, Jim If both…

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Q: 8. HX-NG-200.- 100), which of the following is FALSE A PIX 214 = area of the unshaded region C POX…

A: Given that  The data is normally distributed  Mean (μ)=200 Variance (σ2) = 100 Standard deviation…

Q: Suppose d(10!*x) = 2700, here x is another integer. What is the minimum possible value of x? Here…

A: given : Suppose d(10!*x) = 2700, here x is another integer and  gcd(10!, x) =1.

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

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Q: Let ECR. A point a E R is called a cluster point of E if En(a-r, a+r) contains infinitely many…

A: Given: E is bounded infinite subset of ℝ. To prove: E has at least one cluster point.

Q: 6. Describe the left cosets of SL2(R) in GL₂(R). What is the index of SL₂(R) in GL₂(R)?

A: The left coset for a group G with a subgroup H, tis defined by . Since  can be changed; therefore,…

Q: with Zeros of 2i with integer coeRficients that haf E Puno

A: We need to find the polynomial of degree three with integer coefficient

Q: Tell whether each of the following questions is biased or fair. Why? a. What type of music do you…

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Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

A:

Q: 3) Find L{2re*} using two methods.

A: One method is by using formula and derive whole solution. 2nd method is direct method by using…

Q: ;0<x<0, - 0 <0 <0 Let X,,X,X,r(x;e)=- e.w Discuss the sufficiency by using Factorization Theorem.

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Q: SHOW that the topologies of the & TRK are Not Comparable.

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Q: Derive the foYonala cash" X-In(X+x )

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Q: V = M2x2 (R) let M = { A€ V A = A²} N = { A = V A = -A ² } Subset of the vector space V V = MON…

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Q: 1.) (2a* –be)(ša² +3bc) (x*y-5z')(x*y–42*) 2.)

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Q: In(3*+2*) Apply L'Hospital's theorem to evaluate Lt X00

A: Here we will solve the given limit by L'Hospital Theorem,

Q: 2. 2) tan- 1 4) sin- 6) tan-1 V3 -1 01_ V3 10) sin -1 2. 12) tan-! 3.

A:

Q: FX)= (x-4)²

A: Note: - “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Consider periodic funch'on with pe2 a even f(x) = 2+ēX %3D using tee periodic funchions propechies,…

A: Since it is a period even function, now follow the steps below.

Q: {1 - - :n e N}. Find all cluster points of (a) Let A be the subset of R defined by A := (-1)" A and…

A: Hi! You have posted multiple questions. We will be answering only the first question as per the…

Q: How many shortest lattice paths start at (2, 2) and a. end at (10, 10)? b. end at (10, 10) and pass…

A: Note: As per our guidelines, we are supposed to answer only 3subparts and rest can be reposted.…

Q: If P divides OA internally in the ratio λ₁ : λ2 and Q divides OA extrnally in the ratio λ₁ : λ2,…

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Q: a) Compute the quotient (22 + 2i) / (2 + 2i) b) Suppose z = (In 2) + i (pi/2). Compute e^z

A: " Since you have posted two questions, we will solve first question for you. To get another question…

Q: 7) Show that lim = 1. 200 (z-i)3

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Q: Two RVs X and Y have the joint characteristic function ø.y (@1, 02) exp (-2 w† – 8 ož). Show that X…

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Q: Which formulas are tautologies? Select all that apply. (p-q)-(p¬q) O-(-piq) pvp O-(-p^ (pv q)) → q

A: The given formulas are p→q↔¬p∧¬q, ¬¬p∧q, p∨q and ¬¬p∧p∨q→q. To determine which formulas are…

Q: Prove that : ₁F₁ (u:c: x)]=(-1)" (c-a) „‚e¯x;F₁ (a;c+m; 5). 1 1 (0) "" [~~* 2 098 PRO dx

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Q: The population of a town grows at a rate proportional to the population present at time t. The…

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Q: Use the Successive Approximation Method, to find correct to tigures a real root oF the fun čtion…

A: The given equation,extanx-1=0

Q: Find the FOURIER Scrics FOR the qiuen F Gx) = 18 -ヤEXトO ○と XCT PCメキてび)= FCx)

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Q: show all th work with correct ans

A: [10  -10  -15]ATA=[-10  20   20]          [-15  20  25]               [10  -10…

Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.