(a) Use Maclaurin polynomials to write the following expressions in the form of a degree 2 polynomial with Landau's O remainder as r → 0. i. 1- cos ii. In(1+x) – x iii. cos(2.r) – (1+ x)?

Q: Given a function f(x). Suppose that Newton's interpolating polynomial P₂ (x) of f(x) at the points…

A:

Q: The first three Legendre polynomials are 1, x, and x2 - ½. Choose c so that the fourth polynomial x3…

A: The first three Legendre polynomials are 1,x,x2-12. The fourth polynomial is x3-cx which is…

Q: Evaluate the expression (In (3.34)- tan (61.010)-2)/(5.011e0.37 +1)

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: Use De Moivre's Theorem to find the fourth root of Z = 8i(3 + v2).

A:

Q: Evaluate the given complex function f at the indicated point: *-2i f(z)=r+icos2(θ

A: Given complex number is -2i comparing with a+bi  we get  a=0, b=-2 find the modulus r given by…

Q: What are the rational roots of the polynomial P(x) = æ³ + 3a? + æ – 1? * = -1 O a = 0, a = ±1 Oæ =…

A: P(x)=x3+3x2+x-1 To find the rational roots of the polynomial To select correct option

Q: Ex:. Find the fourth roots of Z=-di Say no 4 K = 0₁12₂3

A: given z=-8i To find the fourth root of the given complex number proceed as follows comparing the…

Q: Construct Lagrange interpolating polynomials for the following functions. f(x)= sin(In.x), x, = 2.0,…

A: Lagrange's interpolation formula for n points can be defined as:…

Q: Which of the following is equal to cos A cos B? 1 [A] [sin(4 + B) – sin(A – B)] 1 [B] [sin(A + B) +…

A: Use trigonometric identities.

Q: 9. Two zeros of f(x) = x* – 7x³ +x² – 63x – 72 are 3i and 8. In what form are the other roots? A. 1…

A: Topic = Polynomial

Q: W laLer Prove the polynomial identity below: (2 – 4y² )² + (4zy)² = (z² + 4y)

A:

Q: Use the Residue Theorem to show that sin²x ㅠ f² = 0 x2 dx = FIN 2

A:

Q: For f(r) sin(Tx) on [0, 1], find the Bernstein polynomials B1, B2, B3, B4. Simplify answers as much…

A: We will find out the required value.

Q: Read the following and answer accordingly: (a) Find an interpolating polynomial of appropriate…

A: fx=sinx x       fx    First order divided difference        Second order divided difference 0…

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Evaluate [3(4-j4) + (j3)(++j4)]tan (4-6i)

A:

Q: Write the equation for the following function: 10 9. 8 7. 4 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 2 3 4 5…

A: we know that equation of a line using two points(x1,y1) and (x2,y2) is gievn…

Q: for f (x) = cosx + sinx function; (Table attached in to description) table is given. a) Find the…

A:

Q: Q.7 Show that B(x,x+)= (2)ª B(2x + 2x)

A: we know that Bp,q=2∫0π2sinθ2p-1cosθ2q-1dθ ......i First, taking R.H.S: Let us take p=q=2x…

Q: Sketch the graphs of y = sin(x) and y = x and determine the unique root, x∗, of the function f(x) =…

A: To find the multiplicity of the root of f(x)=x−sin(x) in the interval [−π/2,π/2], we can follow…

Q: Construct the Lagrange interpolating polynomials for the following function f(x) = e2* cos 3x, xo Xo…

A: Formula for Lagrange interpolating polynomial calculation is:…

Q: b) Show that P1(cos(0)) and P2(cos(0)) are orthogonal to each other, P, and P2 being Legendre…

A:

Q: 1. for f (x) = cosx + sinx function; (Table attached in to description) table is given. a) Find…

A:

Q: (d) (e) Write down the interpolation error term for the above polynomial, and identify the…

A: Given: fx= sin x Nodes: 0, π2, π, 3π2  To find: d) Error term for the given polynomial and identify…

Q: 1. Using x, = 1,x1 = 2,x2 = 3, and x3 = 4, find the Lagrange interpolating polynomial of In(x + 1).

A: Given function is f(x)=ln(x+1) Evaluate value of function at given set of points: x 1 2 3 4…

Q: - Find the zero and its order for the function f(2)=1-Ti+Z+e.

A: Note: If W is the Lambert function then Wxex=x

Q: 6. How many negative real zeros does the function f(x) = 625 - + 8x2 - 20 200 - O O or 2 O 1 or 3

A: