Q1. If n=3, expand µ = a"x;x¡ Q2. Write out the expression Tki (n=4) in full. Which are free and which are dummy indices?

Q: Find n, where (x²+ ax+)² o(x"). Hint: expand (x*+ax+J

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Q: Suppose we have some approximation N(h) to M, and we know that N(h) = M + C¡h+ C2h² + C3h³ +0 (h*) .…

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Q: If F(K,L) =InK?+InL², compute FL(1, 1). Enter the answer in the space provided. If your answer is…

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Q: Find simpler expressions for the quantities in Exercise

A: Use the relation between exponential function and logarithmic function a.) 2 ln e 2 ln e = 2 ln e12…

Q: Calculate M, for f(x) = 6 · In(æ³) over [1, 2]. M6 ||

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Q: Suppose f"(x) = N;(h) + a,h +a,h* +azh +- %3D ... When calculatıng N, (h) using Richardson…

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Q: For any n e N, let An = {x € R | –n <x < n}. Prove that NneN An = A1. (Recall that we define 0 ¢ N.)

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Q: eferaine the radiea) of the constint e for whichiscentinuos on Eo, 00) if n<a 2n +4,if Y2

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Q: B. Find e in the whole number. 1. N = 5,000 2. N = 20,000 3. N = 12,000 and n = 200 and n = 3,000 e…

A: B. Here we have to find e in whole number. Formula to calculate e is as,…

Q: For each n e N, let A, = (}, } + ) %3D Find Unen An. Find Nnen An.

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Q: : Answer the following 1- Let s = = {+:n € N}. Find max(s), min(s), sup(s), inf(s).

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Q: Consider the following conditions. X = 39.46 O = 5.83 n = 65 Test the hypothesis that Họ: H = 42…

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Q: Part 1 of 5 (a) When a = 0.10 and n= 22, Xieft 11.591 = 32.671 Kright Part: 1/5 Part 2 of 5 (b) When…

A: a)GIvenα=0.10n=22

Q: and g(n) is O(H), the

A: Given: f(n)=O(n2) and g(n)=O(n) We have to check that given statement is true or false.

Q: 1 Compute the quantity, w, using w= - 1 w•w - 7

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Q: Let X - N(H, o). Show that the MGF of X is etu+to²

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Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

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Q: Q3: Prove that (9":n e Z) (3":ne Z) but (9":n E Z) (3":n E Z).

A: We have to prove that 9n:n∈ℤ⊆3n:n∈ℤ but 9n:n∈ℤ≠3n:n∈ℤ

Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

A: We are given that   Sn = ∑k=1n1/k   and n&gt;1              ..(i) We have to show that Sn  is not an…

Q: For x=e6t y=531, find y" when y=1- - In 5 ( In 5- 2) 4 - (In 5- 1) 12 O 3 - In 5 (In 5- 2) 2 - (In…

A: topic - derivatives

Q: for n>2, 5 . Deermine for whpch n, n2-2 let |anlく,

A: Given  an = 5nn2-2

Q: 1. Prove with the usual notations that: (a) EV = VE = A (b) A +V =- (c) A= SE Apply the suitable…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: the textbook. Then: A10 (i) Reading Questions: 1. Why we cannot say that r = Vr²? Give an example…

A: The given equation is x=x2 also the modulus of x is x=x2 then negative x could also be taken as…

Q: Show that for any n E N, 7(15".

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Q: What is the general rule to evaluate I N,where N is any positive

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Q: 12. If IN = 2x + 10 and AT = 26, find x. %3D %3D В 丰 N A O 6 O 12 О 10 8. -

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Q: If 2 ak =2 and 2 br = 24, find the following values. k = 1 k= 1 n n 5ak. Σ E (ak + bk). E (@k - bx).…

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Q: Choose the correct definition of from below. O A. kl(n- k)! n! O B. kl(k-n)! k! c. nl(n- K) O D. (n…

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Q: a n eln t--+

A: Given a function : h(x)=31-2x+2 We need to find the graph of this function.

Q: Show that E [(X-µ)^n]=0 for ∀n, with X~N(µ, σ²) and n≥3 being odd numbers.

A: We need to show; E[(X-μ)n]=0 for ∀n and n≥3 being odd numberswhere;X~Normal(μ,σ2) That is, we need…

Q: a) Suppose, T(n) = 1²+2²+3²+..+n2. Show that, T(n) is in O(n³). %3D .....

A: Big-⊖Notation: Let f and g be real valued functions and assume g is eventually position. We say that…

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: Find the Gomplex sdutiona to the e/s 4. (You maly expres the latems in Gmiblex Polat fom).

A: We need to find the complex solutions corresponding to z4-[(1+i)/√2]=0. The solution needed to be…

Q: Apply Gauss forward interpolation formula to obtained y(39) if 15 30 45 60 75 90 Y : 0.23 0.32 0.33…

A: Thanks for your question. Since your question contains two parts, so we are solving the first part…

Q: 9 Find A and A by Hamilt on Hheoren For A=|° E12s -75 -IS

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Q: 1.N= 2500, e = 0.05 2.N= 486, e = 0.01 3. N=930, e = 0.1 %3D %3D

A: Population is a set of elements or subjects for which the study is conducted and a researchers want…

Q: Use MAPLE b A compute whene A is S3 S 31 9732 A2 75 3 D O

A: The MAPLE Code and output are given below.

Q: 1 Compute the quantity, w, using w = W •W - 4 - 5 LO

A: The given vector is w=2-4-5. We know that if a=a1a2a3 and b=b1b2b3 are two vectors, then the dot…

Q: 9 /Find A and A by Hamilt on Hheorem for A= E125 -75 -IS

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Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: If k = 3, df = 12, MSWithin = 45.33, n = 12, and alpha is set at .05, what is the value of Tukey's…

A: From the provided information, k = 3, df = 12, MSwithin = 45.33 and n = 12 Level of significance (α)…

Q: Suppose that these 6 measurements are respectively labeled x,, x2, ., X6. Compute the following. 6.…

A: It is given that x1 = 14, x2 = 17, x3 = 15, x4 = 5, x5 = 7, and x6 = 18

Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: See attached

A: Differentiating both sides with respect to t, we get Now, we find critical numbers of N(t)

Q: If var(e) → 0 as n → 0, then 8 is said to be

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Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: If det A= 0 why is det A+ = O? If A has rank r, why does A+ have rank r?

A: Given Data det A=0   Suppose the column and row of the matrix are linearly independent. The matrix…

Q: Evaluate n e? dz where c:z-1=3 (z+1)

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Q: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: (35 Show that the following grephes are Hameltonian 8) e a) d c) a ol

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.