a) Get the (2n+1)x Pn (x) = (n +1) Prar tx) +o Pau (x) reconnection polynomials using the; P(x, 2)= (1-2 xa +2?)-/2_ E Pn(x)g^ generotór function of Le gendre b) Show that; m #n for S Pm (x) Pn (xld x -Q <-1 Notei Legendre equation; (1-x²) pm lx) – 2×Pm (x) + mlmeo Pm Cx) z o

Q: Show that x = 1 is the only zero of the polynomial x^25 − 1 over Z_37

A: The elements of the sets Z37 are {0,1,2,3,.......,36}

Q: . If f(x) = - x and g a) (f + g)(x) = \\+2x (4-x)+(3x+7) = 11 + 2x c) (f. g)(x) = (4-x)-(3x+²7)…

A: We are given the functions and we need to find out the following functions as given in the question.

Q: Let p1 (x) be the interpolating polynomial of f(x) at xo = 4 and x1 = 5. Then, the error term in…

A:

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: Given the polynomial f(x) = -2x7 + 4x³ + 4.x³ following) а) 10 determine the end behavior of f…

A: see the attached file for a step-by-step explanation of end of the behavior of a function 'f'.

Q: Suppose that p(x) = x^3+ ax^2 + x + 1 has a zero at x = 1, where a is some constant. Determine a,…

A: given p(x)=x3+ax2+x+1 has zero at x=1 Therefore substitute x=1 and equate with 0…

Q: a2f ду? 1 If f(x, y, z) = - 2+y² + find ax2 az2

A:

Q: 11) Suppose that B, (fix) be the Bernsten polynomial. Then ((B₂B)(t.:x) = (b) x (c) x² (d) No Answer…

A:

Q: Let f(x) = e^x. Find the polynomial P2(x) of degree at most 2 such that P2(1) = f(1), P2(2) = f(2),…

A: We have to find the polynomial of degree 2 for the function fx=ex using the divided difference…

Q: Indicate the least integer n for which f(x) is O(x¹) if (4x³+2)(8+3) f(x) = +1

A:

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x)=2x+5 t(x)=3x…

A: Step 1: Given functions: s(x)=2x+5, t(x)=3xwe have to find the expressions: (s⋅t)(x), (s+t)(x), and…

Q: Let 7 (t) = Find 7 (t) デ'(t) =D<

A: r'(t) =d(r(t))/dt

Q: Define the upper bound for the error in a Chebyshev polynomial?

A: To Define: An upper bound for the Chebyshev polyomial.

Q: hd the invense transformof eack of t FX) 6x-5 FCx)=

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

Q: Find the following using the rule indicated (only): i) If f(x) = (6x? – 8) (3x + 2), find f'(3)…

A:

Q: Q3. Using interpolation, approximate the following function by a polynomial of degree at most 3…

A:

Q: Show that the polynomial p(x) = -x^3+x^2+1 has a root in [1,2]

A: We can check for the values of p(x) :

Q: Assume that M = N₁(h) + a₁h² + a₂hª + azh6 + ... Then using Richardson extrapolation N4 (h) is of…

A: Use Richardson's extrapolation formula for even power series, to obtain the solution.…

Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ |

A: find the polynomial f(x) for which  x fx-1=x-3 fx ∀x for x=0 x fx-1=x-3 fx ∀x

Q: Write a polynomial function in standard form with zeros at 2, 4, and 5. 0 (2) = 2 382 + 11a 40 %3D…

A:

Q: Q No 4 Evaluate (a) S 3x+4x+16x+20x+9dx (x+2)(x²+3)²

A: NOTE- I HAVE ANSWERED FIRST QUESTIO FOR YOU. IF YOU WANT THE SOLUTION OF REMAINING QUESTIONS THEN…

Q: Find a polynomial p(x) = ao + a1x + aza² + azx³ of degree < 3 (here ao, a1, a2, a3 are real numbers)…

A: In this question , use the given values and solve the equations and find the polynomial.

Q: Let i, j ∈ Za and w, x ∈ Zb with i, j different from each other and w, x different from each other.…

A: Say, the total number of elements in Za = m, the total number of elements in Zb = n,  The total…

Q: Let A = B = C = {x 1 x is a real number}. Let f: A → B and g: B → C be defined as follows: f(a) 2a…

A:

Q: Let f(x) = 2x 6x +5 then f(x) is concave down on Select one: O a. (-0,0) O b. (-00, 1) O c. (1, 0) O…

A: We can make it easier for you

Q: x = 1,2,3 f(x) = 4,5, 9 Interpolate a polynomial by using above data with lagrange inerpolation

A: The given data is  x 1 2 3 fx 4 5 9 We have to find the interpolation of a polynomial by…

Q: Letflx): 3x-2:9 x)=5x+1 Compute the indicated Values, a, lfogl (3) blfef) (oJ d, (gog) (-7) )e.…

A:

Q: 9) suppose that horx)=1, f,(x)=x ond dz(X) Prove that Ba(f, - where Ba is a Bernyterh Polymomial.

A: Given functions are f0(x)=1, f1(x)=x and f2(x)=x2 Since Bernstein polynomial is…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.