11. Let f (x) E Z[x] with deg (f(x)) > 1. Let f'(x) be the polynomial in Zp,p € Z, obtained from f(x) by reducing all the coefficients of f(x) modulo p. Assume that deg (f(x)) = deg(f(x)), then: a) If f(x) is reducible over Zp, then f(x) is reducible over Q b) If f(x) is irreducible over Zp, then f(x) is irreducible over Q c) If f(x) is reducible over Q, then f(x) is irreducible over Z, d) None of the above

Q: 10. If a Taylor polynomial of f (x) = In In (x – 1) can be used to approximate In1.2, what should be…

A: Given: fx=lnx-1  ……1   To find: Centre of Taylor expansion for ln 1.2

Q: 4. Determine the first and second degree Taylor polynomial approximations, L(x, y) and Q(r, y), for…

A:

Q: Let f (x) = cos(2x) + 7. Compute the following Taylor polynomials of f. For any approximations, you…

A: From the given problem:   fx=cos2x+7   Let centered at a=0.   From the Taylor series:…

Q: Use the second Taylor polynomial P2(x) for f(x) = r? + cos(x) about co = 0 and evaluate S f(x)dx.

A: Given: fx=x2+cosx The second degree Taylor polynomial about x0=0 is P2x=f0+f'0x+f''02x2. Here,…

Q: Let fn E D[0, 1]. Suppose that fh g on [0, 1], and lim fn(1/2) exists. For each x E [0, 1], show…

A:

Q: Find the 5th degree Taylor Polynomial for f(x) = sin x centered at C = 4

A: Given - f(x)=sin x centered at c=3π4 We need to find 5th degree Taylor polynomial. Taylor polynomial…

Q: 5.4 Compute the Taylor polynomials Tn, n = 0, ..., 5 of f(x) = sin(x) + cos(x) at xo = 0.

A: Solve by Taylor theorem

Q: Find a formula for the n-th term of the Taylor polynomial for f(x) = ln(x) centered at x = 1.

A: given function f(x) = lnx centered at x=1 so formula for n-th term of the taylor polynomial:-

Q: 5. Write a 5th degree Taylor polynomial for f(x) = cos(2x) centered at x = T/4. %3D

A:

Q: 3.10 Show that an arbitrary function f(x) can be expanded on the interval 0<xsa in a modified…

A: Let f(x)=∑AnJYyrnxa Now multiply both sides by x JYyrmxa , x f(x) Jvyrmxa=∑x AnJvyrmxaJvyrnxa Now…

Q: Find the third degree Taylor polynomial of f(x)= /x centered at x=1.

A: First, let's understand The Taylor series Expansion of any polynomial and the meaning of…

Q: Find the coefficient of degree 2 in Taylor polynomial for f(x) = In (1+ rx) about x = = 1.

A: To find the coefficient of degree 2 in Taylor polynomial for the give function- f(x)=ln(1+rx) about…

Q: A continuous r.v. F(x1= === 2 × -IN 15 X has CDF X Co OBX C1 18X 16 17 **** 18

A: Given: Fx=0            x&lt;012x        0≤x&lt;1k            x≥1

Q: d x"J,(x)=-x"Jns(x) d, n+1 X.

A:

Q: ind the Taylor polynomial of degree 2 centered at a=π that approximates f(x)=cos(5x) P2(x)=

A:

Q: Find the best rank 2 approximation to A from (1) with respect to ||:||F.

A:

Q: What is the minimum order of the Taylor polynomial centered at 0 for cos x required to 10-42

A: Given,        cos(-0.35) with an absolute error no greater than 10-4.

Q: Give the Taylor polynomial of order n e N about 0 for f(x) = e".

A: We have to give the Taylor polynomial of order n∈ℕ about 0 for fx=ex

Q: Find the nth Taylor polynomial for the function f(x) = ln x, n = 4, centered at c = 2.

A:

Q: 1: Let f(x) =2x+3 cos x-e', Osxs1 a. Find 3rd Taylor polynomial, and use it to approximate f (0.2).…

A:

Q: 3. Find the fifth Taylor Polynomial for f(x) = In x around 1. 4. Expand f (x) = --1 around a = 0, to…

A: (3) From Taylor's polynomial around x = 1 is given by,…

Q: Compute the least squares quadratic polynomial p2(x) which gives the best fit to e x over the…

A: We need to find two things, A least square quadratic polynomial p2(x) which gives the best fit to…

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

A:

Q: 2. Determine the 1st and 2nd degree Taylor polynomials L(x,y) and Q(x,y) for f(x, y) = tan¬1 (x +…

A: By Taylor series  we get,  L(x,y)=fx0,y0+x-x0 ∂f∂xx0,y0.∂f∂xx0,y0+y-y0∂fy0x0,y0and…

Q: Find the fourth degree Taylor polynomial, T4(x), for f(x) at -: Que f(x) = 3 sin(x) Que a) Find the…

A: We have to find Taylor polynomial

Q: Find the nth Taylor polynomial centered at c. f(x) = ln(x), n = 4, c = 6 P4(x) = X

A:

Q: Find the degree n=4 Taylor polynomial for f(x) = ln (x + 1) at c=1.

A: The degree n=4 Taylor polynomial for f(x) at c is given by f(x) = f(c) + f(1)(c)1!(x-c) +…

Q: From Rogawski ET 2e section 8.4, exercise 1. Calculate the Taylor polynomials T2(x) and T3(x)…

A:

Q: Find the degree  2 Taylor polynomial T2(x) for f(x) = tan x centered at x = π/3

A: First, we will find the general Taylor series of f(x) = tan x centered at x = π/3. We know that…

Q: Find the Taylor polynomial of degree four for the function f(x) = x'/4 at z = 1.

A: Solution:

Q: 4. Show that the Taylor polynomials for f(x) = In(1 + x) can be used to approximate f(s) for s e…

A:

Q: Approximate the function f(x) = ln(1+3x) by a Taylor polynomial of degree 3 at a = 1 %3D

A: (a) The given function is fx=ln1+3x and a=1. Now differentiating it with respect to x.…

Q: 1. Find the third Taylor polynomial P(x) for the function f(x)= 2x cos (2x)-(x-2)* about X, = 0.…

A:

Q: Let f (x) = cos(6x) + 7. Compute the following Taylor polynomials of f. For any approximations, you…

A:

Q: 5. Find the n-th Taylor polynomials for f(x) = 1 about x = 3 and express x + 2 it in sigma notation.

A:

Q: Find the fifth Taylor Polynomial for f(x) = ln x around 1.

A:

Q: let f(x) = cos(x) and x0 = 0. Find the Taylor polynomial of degree N = 4.

A:

Q: Find the residue at z = 0 of the function 1 / (z + z^2)

A:

Q: Let f (x) = cos(6x) + 7. Compute the following Taylor polynomials of f. For any approximations, you…

A: Given  functions fx=cos6x+7

Q: Consider the function f(x) : 1 defined on (-∞, 2) U (2, ∞). x – 2' Find the Taylor polynomial of…

A:

Q: Compute the Taylor polynomial T5 (x) for f (x) = cos(x) around a = 0 and use the Error Bound to find…

A:

Q: Consider the R – R function f defined by f (x) = e* ln x. ine the third order Taylor polynomial T3…

A:

Q: 5. Compute the 1st and 2nd degree Taylor polynomials L(r, y) and Q(r, y) for f(r, y) = In(r² + y?)…

A: 5 Given function is fx,y=lnx2+y2. We have to find the 1st and 2nd degree Taylor polynomial Lx,y and…

Q: Let f(x) = [* log(1 +t) dt. %3D t Give a Taylor polynomial of degree n for f about a = 0.

A: The Taylor series of log(1+t) is:…

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

A:

Q: Find the Taylor polynomial of degree two approximating the given function centered at the given…

A: We have to solve

Q: Determine the nth Taylor polynomial for f(x) = e^x at x = 0.

A: To Determine: nth taylor polynomial for fx=ex at x=0

Q: Suppose f and g are C" functions with Taylor expansions denoted Ta(f, xo, x) and T,(9, xo, x). Prove…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 2) For a random variable X, its kth-order moment is defined as E(X*). Given the p.d.f. fx(x) of X,…

A: Given, for a random variable X, its kth order moment is defined as EXk and its Fourier transform…