Approximate Lf (P) = Uf (P) = 10 √6²⁰ |× - 9 | x - 9 dx, by computing Lf (P) and Uf (P) for the partition P = {8, 8.5, 9, 9.5, 10}.

Q: Q1-Using the nodes (x, =2, x-=2.5 and x; =4), to find the second interpolation polynomial for flx) =

A: Given nodes are x0=2, x1=2.5, x2=4 and function is f(x)=1x Now table is x 2 2.5 4 f(x) 0.5 0.4…

Q: For f(x) = (x + 3)*(x – 6)³(x + 5), list each real zero and its multiplicity.

A: Given function is f(x)=x+34x-63x+5

Q: What is the coefficient of xy³ when (2y-x)° is expanded by the binomial theorem?

A:

Q: The interpolating polynomial p(x) of degree 2 of f(x) = 6xª – 2x³ + x² + 9 is p(x) = x² + 9. %3D…

A:

Q: How do you multiply

A: Given radical expression is,

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

A:

Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: Let P(x)=-x²³+2x2-6x'-5x'-1 and D(x)=x+1 Determine the remainder when P(x) is divided by D(x)

A: The given polynomial is:Px=-x23+2x12-6x7-5x4-1Dx=x+1To find the remainder.

Q: Consider the data (1,10), (3,6)(1,10), (3,6). Then, Newton's polynomial that interpolates the data…

A: Solution of given problem is followed by Newton's interpolation formula.

Q: Show that the multiplicity of (x-1) is 1.

A:

Q: (d) Compute P(x 2 2).

A: Given that  X~Poisson(μ=6) Probability mass function of X is  f(x)=μxe-μ/x!  , x=0,1,2,3,____

Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: In(x) dr. x² + 9'

A: Sol

Q: USE SYNTHETIC DIVISION 16 x4 17 x2 2x - 6 ÷ x – 2 -

A: Solving the problem by finding the results.

Q: Indicate the least integer n for which (3x6 + 2x2)(x3 + 3x) is O(xn).

A: Solution:-

Q: Determine Q(x) when P(x)=x³-5x2-3x+2 is divided by x-1 and then expressed in the form Select one: O…

A:

Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

Q: Prove that (p – q)× (p+q)= 2(p×q)

A:

Q: If P(x) = x2 + x + 1, find P(7). P(7) =

A: Given that  P(x)=x^2+x+1  To find the P(7)

Q: Is z(√2) isomorphic to z(√3)?

A:

Q: 1. [K2] Without dividing, determine the remainder when P(x) = 10x3 – 9x2 – 8x + 11 is divided by 5x…

A: We use remainder theorem for calculating the remainder.

Q: For the polynomials p(x)=4x* – 3x² +x -1 and d(x) =x² – 1, write in the form p(x)= d(x)q(x)+r(x).

A:

Q: 6.S ke ten the Cate given by Poiar eq dot;in )=v=2S16 %3D fb r=2+ Cos o and Campute the arer boundad…

A: We have to sketch the given Polar curve. And find the area bounded by Polar curve.

Q: 5. (x5 + 25x3 -7x2 +37x 18) + (*+5) %3D II. A. Use the REMAINDER THEOREM to find the remainder of…

A: We have to solve

Q: find all polynomials P(x) and Q(x) satisfying, for all x∈R the equalities: P(Q(x))=x4-5x2+7 and…

A:

Q: For a data set {xi, yi ; i=1,n}, which of the following conditions must be satisfied by an…

A:

Q: Construct the addition table for Z5. Using this table, or otherwise, determine the following x in…

A: First we find addition table for Z5. Then find values of x.

Q: - Express P(x) = xª +.2x³ + 2x² - x - 3 in terms of Legendre's polynomials

A: In this problem, we use Rodrigue's formula to express Legendre's polynomials.

Q: Given h(x)= 2x' – 5x – 15x? + 31x +15: %3D

A:

Q: If P(x) = x +x+ 4, find P(8). P(8) =D

A:

Q: Let P (x) = 2x - 15a + az?+ bx + c, where a, %3D Given that (x - 5) is a factor of P (r), find a…

A: It is given that,  P(x) = 2x4 - 15x3 + ax2 + bx + c It is given that, (x - 5) is a factor of P(x).