Expand using Taylor upto four termns f((ntaih Ynt a k) senes

Q: Y Cn) be defined recursively by Let YCO) = 3, Y (1)=4 and Ycn) =3Y(a-1) – 2 Y(n-2) Ynz2. Y (n)= 2^+2…

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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: OShow that in 27 and use Soot method has bisection approximation to the Soot * at leest within a the…

A: The given equation is. fx=x3+4x2-10=0 fx=x3+4x2-10 To find the root in the interval 1,2 that is…

Q: 6) The Ying of integers(2) is ideal of veal number (R) an DTrue D Fulse

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Q: Use AAS to prove th Given: ZR and ZP a QR || SP

A: Given that, ∠R and ∠P are right angles. QR¯∥SP¯ We have to prove that, △QPS≅△SRQ

Q: fired supremum of As 3n +2 Inew y. 2nt/ Prove your arswer

A: This problem is based on finding the supremum.

Q: 6. Find the Maclaurin seriés for f(r) = (1-x)-2. %3D

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Q: gorean Theorem. 12m 14m

A: Topic pythagoras Therorem

Q: こ be terms Prove Find o of ů, ů. your resubts . in

A: Consider the given vectors: Here the objective is to find the vector w such that

Q: Compute 4n — бп? lim Vlan| for a,n %3D 3n2 +7 n-00

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Q: Find the area of the inner loop ofr= 3+4cose. 0.7612 0.4775 O 0.9551 O 0.3806

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Q: Prove by the indirect method: Given: AMPN is not isosceles Prove: PM + PN

A: Concept used: Step of indirect proof: First assume opposite of conclusion of the statement. After…

Q: 1. Let, a1 = 7 and for n 2, an An-1 express an in terms ofn. %3D ". **

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Q: 1 Expand in ascending powers of x, up to and including the term in x', simplifying the V(1 –2x)…

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Q: Use Simpsons 1/3 rule to evaluate of e-x2 over the interval 0.2 to 1.5 using 6 segments ?

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Q: Find a number t such that In(4t + 3) = 5 %3D

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Q: 1. Apply Parseval's theorem to Q(t)= -{Q(+27) and use it to evaluate a sum rule for Σ1 k=1 |t| <T…

A: Dear Student, Since you have asked multiple questions, I will solve the first question for you. If…

Q: Q: Prove that tim %3D

A: We have to prove the limit

Q: Prove by induction that 1 2. Prove that (xn) is contractive and thus convergent. Compute lim (xn).

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Q: SHOW by Induction that : Alx)" /1-(1-2x)" A For all n e IN" from A (aS is a matix) obseivation Where…

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Q: Ex: @ write out the expessien R(n=4) jki in full. wuich aue free and which ane dummy indices ?…

A: We write expression of curvature Tensor

Q: such that ab = 1 b) : In Z3XU3, Find the order of (1, 2). Show your work.

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Q: Let 9,n be antegers wth 2n and ged (a,n)=1. Show tht of U(Z.) ={a*+nZ:tez} then o#1 mod 6) for all…

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Q: For for any pestive integor n Show that %3DFHE nth fibonacci term fn=the

A: We need to show that , for any positive integer n ,  f1 f2 + f2 f3 + ....... + f2n-1 f2n = f2n2…

Q: Prove for uniform covergence the series 1 „VxeR. (By using Weierstass's M-test). 5 7 2 n=1 n" +n'x?

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Q: Compute 32+n21-3n n=0 If this is divergent, input "O" as your answer If applicable, submit answers…

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Q: Prove the following in Z[i]: if a y and 3|y with a and B relatively prime then aß | y. in

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Q: k+ln k > ak, where aj = and ak+1 ak k+10 %3D k=1

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Q: Determine if the veetor is in Spanis} where S-3,01,2,0L3,4,2, 183 Ifit is, write T as a linear…

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Q: Showthat S subring of RIKRZ+R3

A: For the solution of the problem follow the next step.

Q: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

Q: Find the Taylor expansion of 1/z² for points inside the circle |z – 2| < 2.

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Q: Find the Radus of convegnce Rand the niterral of Convegua I of the Taylor senes (12, (x+1) n(2n=1)…

A: The given series is: ∑n=1∞ (x+1)2nn(2n-1) 4n

Q: *show tht the fanetion fW=$- satify The by PotheseI of Rolshe oren- on [0,4]

A: For the solution follow the next step.

Q: 2.2.6. In the text, the modulus is defined in terms of the inner product. Prove that this can be…

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Q: (c) Evaluate d Gosh: where C: |z| = 2 by using Cauchy's residue theorem.

A: Given integral is ∮C dzcoshz;   C : z=2 As, we know  If z = x+ iy then z =x2+y2 As given that  z=2…

Q: 5. Use Cauchy's Residue theorem to evaluate dz; Có lz-il =1 (2+1)

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Q: Evaluate det(A) by a cofactor expansion along a row or column of your choice. 3 0 0 1 0] 4 4 4 1 0

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Q: 7. Use the binomlal theorem to expand (x+x-1] and simplify the result. Show your work.

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Q: U Prave the fallowing by inductions Ta1-or all pastive integes ntl 1.2 2-3' 3.-4 ncnt)

A: Prove for n=1,  Assume the relation is true for n=k and then prove for n=k+1

Q: R Given: OR L ON Prove: ZROT is complementary to ZNOT Proof:

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Q: Let flx)= a cose + 3 Sinse with (o,f to)), (,2) and (T, 2 ). Use Muller's method to find a quachatic…

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Q: Sfind the Taylor secies for (x)= Tx)(+ 3×) Centeredat x=0. Ck X*. That is, revwrite it as kso

A: Solution is as shown in step 2

Q: Nine Starbucks are located in a 3 mile by 3 mile square area in which there is a 1 mile by 1 mile…

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Q: Let (an)1 be a sequence of positive real numbers: a, > 0. Suppose that Sn = > a; diverges. i=1 ai tn…

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Q: 4) defin 4, = 1, a2 = 3 , and an = Cnmy + an-z (n7.3). Prove by indeution on in21 that an < (1.75)*.

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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.