Approximately how many multiplications are needed to evaluate p(x) = a,x" + a,1 Xn-1 + ... + a,x + a, %3D at a given point x = x, using Horner s rule? N" 2n - 1 N2 2n - 1

Q: 49. f(x) = alst %3D n=0 Selet ai 50. f(x) = 2 (-1)+1(x – 5)n n5" n=1 * (- 1)n+1(x – 1)"+1

A: f'(x)=∑n=1∞ (-1)n+1n(x-5)n-1n5n      =∑n=1∞ (-1)n+1(x-5)n-15n Apply the ratio test to check the…

Q: _11. What is Sdx? A. +C B. +x + C х-1 C. c. ++ 2x + C x(2x2+3x+6) + C x3 D. _12. In solving S th dx,…

A:

Q: 0, 0<x<1/n, fn(x) = { /n, 1/n < x < 2/n, 2/n < x<1. 0,

A: Pointwise convergent:- A sequence of function is pointwise convergent, if its every point sequence…

Q: f(x) = 13x- In(7x + 14) %3D has a single critical number at x = A. Find this critical number. A =…

A:

Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

A:

Q: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

A:

Q: 5xdx 3. Find the integral (x-1)3 -5 a. 2(x-1)2 +C b. ++C -5 2(x-1)2 X-1 c. In () – in () + c )-In()…

A:

Q: Let xn ≥ 0 for all n ∈ N. (a) If (xn) → 0, show that (√xn) → 0. (b) If (xn) → x, show that (√xn)…

A:

Q: To find v,(x=0.1) yn-1-0.1+ (0.1)2-1(0.1)" +급(01).-0.909675 To find y2(x=0.2) Expansion around x0 HW…

A:

Q: Vx (1- 2 In 1 1-x/2 | + C A ! In 1 1-x/2 | + C 2. -2 In I 1-x/2 | + C -In 1 1 -x+/2 | + C O A O D E…

A:

Q: max  z =  x1 + 3x2 s.t.      x1 + 2x2 ≥ 6          2x1 +  x2 ≤ 8           x1, x2 ≥ 0 For the LP…

A: A LPP is written in standard form as  max (or min) z = c1x1 + c2x2 + · · ·+ cnxn subject to a11x1 +…

Q: ker(A) = R104 %3D O ker(A) = {0} %3D ker(A) cannot be determined from this information

A:

Q: x,x→X,x mysa rft bns astemee a.s. X→X=Xn→X

A:

Q: -2x dx 7. Evaluate (1–x)' A. x' + 6x - In(1-x)" +, -(1-x)* +C C. x' +6x + In(1-x)' +, (1-x) +c 1-X…

A: See the details solution in below

Q: Expand x?y + 3y – 2 in powers of x + 1 and y – 2. (up to third degree terms).

A: Given :- The given expansion x2y + 3y-2 in powers of x+1 and y-2.

Q: Zn+1 In+2 = 1+ p > 1+p = = i = i, tn+1 1+P7 =i = 2, Z, In+4 > i, Zn+4 < 7.

A: Given system (2) is tn+1 =1+pznzn-12,  zn+1 =1+ptntn-12 ----(2) (System (2) ) For equilibrium point…

Q: x -x 3 Let A=0 x+1 1 X -8 x-1 Ximx101 (A) 3sb = (A)dobyerit ov For what values of x does A-1 exist?…

A:

Q: Rn %3D *ーラ=)+ ニ x²+2 x20 puiy (日 an swere and 4) Find all x for which o>ズ x+S) working f (x) = 9).…

A:

Q: ner method ation 3 on x² +

A: Given function is, x3+x2+xe+2x-1=0

Q: z2-1 What is residue of f (z) = at z=3 ? 8. o Res (f(2), – 3) = %3D 3 None -8 Res (f(z),3) = | %3D…

A:

Q: The total number of additions and multiplications in t= 0 for i := 1 to n for j := 1 to n t = (it +…

A: Given information is:

Q: Which of the following is homogenous of smallest degree? x² + y² A X x-y B C D x-y In x - In y √√x+y

A:

Q: 5 0.6 0.1 Apply Gershgorin's theorem on B = -1 6. -0.1 1 2

A:

Q: Ym - 21 , prove that + (n? m² ) yn =o 2 + (2n+1)x Ynts

A: Given y1/m+y-1/m=2x To prove that  x2-1yn+2+2n+1xyn+1+n2-m2yn=0 Solution :  y1/m+y-1/m=2x…

Q: 2. The value of ₁-² dx = ..., for each Chebyshev polynomial Tn (x), n ≥ 0. 1) 플 b) c) 0 d) None of…

A:

Q: 5/2 5 ds Evaluate the integral V100 -s2 5/2 5 ds %3D V100 - s2 (Type an exact answer, using n as…

A:

Q: 5. (a) Find the real constants P, Q, R, for which 3 P Qx + R x2 – x + 1° x3 + 1 x + 1 | Show that V3…

A: 5(a)  3 / (x3+1) = P/(x+1) + (Qx+R)/(x2-x+1) ......(1) Now, 3/ (x+1)(x2-x+1) = P/(x+1) +…

Q: Let f (n) = n²+ 3 and g(n) = 5n - 11 for n in N. Thus %3D %3D f: N N and g: N→ Z. Calculate f(10) +…

A: To find f(10) + g(10) when fn=n2+3 and gn=5n-11 for all n in N.

Q: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: '12 x2 dx by computing Lf (P) and Uf (P) for the partition P = |-24 Approximate -24, –12, 0, 12 Lf…

A: Given ∫-2412x2dx and Partition is P={-24,-12,0,12}.

Q: 10 Find the linearization L(x) of y = e¹0 In(x) at a = 1. (Use symbolic notation and fractions where…

A: Given:   y = e10 ln(x)  At a = 1

Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

A:

Q: A useful consequence of Taylor's theorem is that: |æ – c|" max|f(n+1)(2)| (n + 1)! > (æ)"y| (1)…

A:

Q: :Use inverse matsix (by Gauss Jordan an Elimination) to solve the syálem 2x + By +3 = - 1 %3D 2x…

A: Consider the given equations 2x+3y+z=-13x+3y+z=12x+4y+z=-2 The given equation can be written as AX=B…

Q: Using OLS or any other suitable method, Prove that E(ß1) = B1

A: Full form of OLS estimator is ordinary least square method. β^1 is the parameter of the model. Under…

Q: 6. What is the coefficient of x'y" in the expansion (4x + 5y) s. Show your work here:

A: We find coefficient of x7y8 in the expansion (4x+5y)15

Q: 5xdx 3. Find the integral (x-1)3 -5 5 а. 2(x-1)2 + C x-1 -5 b. 2(x-1)2 + C x-1 c. In (7DE) – in () +…

A:

Q: Let s(n)-Σ(Δx Ax and simplify. %3D i = 1 Therefore, s(n) = E()ax Дх %3D i = 1 in X 12 7 49 %3D n2 i…

A: Given expression can be simplified as

Q: 9-x2 B: Find the integral o L 18-x2-y2 /x²+y2 xydzdydx.

A:

Q: 13 Approximate x² dx by computing Lf (P) and Uf (P) for the partition P = {-26, –13, 0, 13. -26 LF…

A:

Q: z/(z-3)2 dz ; C: |z+3| =3 slove by residue theorem

A: The given integral is,

Q: 11. [D' +4]y=sinx, using reduction of order and letting y, = vcos2x. (Note: This is the same problem…

A:

Q: QUESTION 11 Determine whether y or y and x y= Sx4+6x 2 -s y as x- y as x Oy as x y as x y as x y as…

A:

Q: Q2) let A = [ 1 find e4t using Gauss-Jordan method.

A: First we will find the eigenvalues and corresponding even vectors of the matrix by Gauss-jordan…

Q: 5. Prove that |e³ – Eosisn l < 32 3n+1 e3 (n+1)!

A: The given problem is to prove the following summation inequality. We have to use taylor series for…

Q: d'y It is given that y=(1+x)² In (1 + x). Find dx 3 Prove by mathematical induction that, for every…

A: First it is required to find

Q: 1. Evaluate the following. Use only the rules and techniques of integration presented in the module.…

A: To evaluate the given integral.

Q: 9- m2 Evaluate S, – m² V9- m2 - n2 8ax (n2 + x2) dx dn dm E A B I E E P Type here to search II

A:

Q: 1. Using Gauss-Seidel and Jacobi Method, find the values of x1, x2 and x3 with ek < 0.001. 2x — 6х,…

A: