Consider the Legendre polynomials of degree n Ph(x) = Σ (-1)m 0

Q: Let g (x, y) = 7 sin(xy) – 9x? In(y) + 4. Find the degree 2 polynomial, p, which best approximates g…

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Q: Let X x b(n,-) and E(3x) = E(3-5.x) find n.

A: Given X ~ B(n, 12) P(X=x)=Cxn px (1-p)n-x; x=0,1,....n…

Q: How do we prove a theorem of the form ∀x(P(x)->Q(x))?

A: To prove the theorem of the form ∀x(P(x)→Q(x)), we apply mainly two steps: 1: We take the arbitrary…

Q: Given the functon /(x) Suppose that the Newton's interpolating polynomial P,(x) of f(x) at the…

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Q: nsider the following. -2x5 + 9x4-7x³ - 12x = 0, [3,4] ) Explain how we know that the given equation…

A: In this question, we will find the solution of the equation.

Q: 2. Find the Maclaurin polynomials of order n=0,1,2 for f(x) = cos(x).

A: Consider the formula for Maclaurin series: Calculate the derivatives to find the terms in the…

Q: Q: If f (x) is a polynomial function of the nth degree prove that fe'f(x) dx =e* {f(x)-f (x)+ f…

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Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: 2) for function f (x) = ln x (Table attached in to description) Table is given. a) Construct the…

A: We can calculate the exact value of ln(x) at x = 2.5 by substituting 2.5 in the place of x in ln(x).…

Q: For a second degree polynomial P such that P(1) = 3, P'(1) = 4, and P"(1) = 6. P(x) =

A: we have to find the second degree polynomial P such that P(1)=3, P'(1)=4 and P''(1)=6. let the…

Q: (xi) f(x)=sin( (xi) f(x) [r] on [0, a] f(x) = 0 for some x between n and n + 1. (ii) f(x)-5r4 +2r…

A: (i) To find an integer n such that f(x)=0 for some x between n and n+1.

Q: Consider the following. 3x4 - 8x + 5 = 0, [2, 3) (a) Explain how we know that the given equation…

A: Given that  3x4−8x3+5=0, 2,3

Q: Show that the Maclaurin polynomials for f (x) = ln(1 + x) are

A: The given function is fx=ln 1+x. fx=ln 1+x f0=0 f'x=11+x f'0=1 f''x=-11+x2 f''0=-1…

Q: Let f(x) = x + 2x - ax + bx (i) Find the values of a and b so that the multiplicity of the root -1…

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Q: 2. (а) Find the function P(x) = a +b cos(n x) +c sin(nx), which interpolates the data 0.5 1 y 4 (b)…

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Q: -Vx2+5 -x f(x): f'(0)? -x+2

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Q: 2) Given: f(x) = (x-1) (x+ 1) was transformed to (x) = (x- 1)(x+ 1)-1. How many roots would the…

A: f(x)=(x-1)2(x+1)2 was transformed to f(x)=(x-1)2(x+1)2-1.

Q: (5) Let f(x) = 5x² + for x > 0, where A is a positive constant. Find the smallest A such that f(x) ≥…

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Q: Determine zeroes and their orders: (a) f(2) = (z +2– i)?; (b) f(2) = 24 – 16; (c) g(z) = e2: – e*;…

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