Numerical Methods
4th Edition
ISBN: 9780495114765
Author: J. Douglas Faires, BURDEN
Publisher: Cengage Learning
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Chapter 2.6, Problem 1E
Find the approximations to within
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Solve and answer the following problems as indicated.1) Determine the quotient q(x) upon dividing f(x) by g(x) ℤ_7[x].f(x) = 5x^4 + 3x^3 + 1g(x) = 3x^2 + 2x + 12) Determine the remainder upon dividing f(x) by g(x) in ℤ_7[x].f(x) = 5x^4 + 3x^3 + 1g(x) = 3x^2 + 2x + 13) Find a nonzero monic polynomial in ℝ[x] of degree 3 whose roots are 6 and 4±i. Write the polynomial as infinite sequence as in the previous items.4) In ℚ[x], using the Euclidean Algorithm find the monic gcd of f and g below. Write the gcd as an infinite sequence as in the previous items.f(x) = x^5 + x^4 + 2x^3 - x^2 - x - 2g(x) = x^4 + 2x^3 + 5x^2 + 4x + 45) For what value of k is x-2 a factor of x^4-5x^3+5x^2+3x+k in ℚ[x]?
Find the Maclaurin polynomial of the ninth degree for the function h(x) = ln(1+x3)
Given f(x) = - 3x ^ 3 - 2x - 4 verify that f(x) is invertible and, if so, find the equation of the tangent line to f ^ - 1 * (x) at the point where x = 24 Note that f(- 2) = 24 .
Chapter 2 Solutions
Numerical Methods
Ch. 2.2 - Use the Bisection method to find p3 for f(x)=xcosx...Ch. 2.2 - Let f(x)=3(x+1)x12(x1). Use the Bisection method...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Use the Bisection method to find solutions...Ch. 2.2 - Sketch the graphs of y=x and y=2sinx. Use the...Ch. 2.2 - Sketch the graphs of y=x and y=tanx. Use the...Ch. 2.2 - Let f(x)=(x+2)(x+1)x(x1)3(x2). To which zero of f...Ch. 2.2 - Let f(x)=(x+2)(x+1)2x(x1)3(x2). To which zero of f...Ch. 2.2 - Use the Bisection method to find an approximation...Ch. 2.2 - Use the Bisection method to find an approximation...
Ch. 2.2 - Find a bound for the number of Bisection method...Ch. 2.2 - Prob. 12ECh. 2.2 - The function defined by f(x)=sinx has zeros at...Ch. 2.3 - Let f(x)=x26,p0=3, and p1=2. Find p3 using each...Ch. 2.3 - Prob. 2ECh. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Use the Secant method to find solutions accurate...Ch. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Use the Secant method to find all four solutions...Ch. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - The fourth-degree polynomial...Ch. 2.3 - The function f(x)=tanx6 has a zero at (1/) arctan...Ch. 2.3 - The sum of two numbers is 20. If each number is...Ch. 2.3 - A trough of length L has a cross section in the...Ch. 2.3 - Prob. 17ECh. 2.4 - Let f(x)=x26 and p0=1. Use Newtons method to find...Ch. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Use Newtons method to find all solutions of...Ch. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.5 - The following sequences are linearly convergent....Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.6 - Find the approximations to within 104 to all the...Ch. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Repeat Exercise 2 using Mullers method.Ch. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Two ladders crisscross an alley of width W. Each...Ch. 2.6 - Prob. 11ECh. 2.6 - Prob. 12E
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- A polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is counted m times.arrow_forwardFor the cubic polynomial function ?(?)=??3+??2+??+?,f(x)=ax3+bx2+cx+d, find ?,a, ?,b, ?,c, and ?d so that 00 is a critical number, ?(0)=5,f(0)=5, and the point (1,1)(1,1) is an inflection point of ?.arrow_forwardA 5-th degree Taylor polynomial of a function f(x) at × = 0 could potentially have the form (select all that apply):A) t(x) = 1 + x + x^2/2! + x^3/3! + x^4/4! +x^5/5! b) t(x) = x c) t(x) = x^6 d) t(x) = x^5arrow_forward
- Factor f(x)=2x^3+5x^2-83x+40 into linear fuctors given that -8 is a zero of f(x) f(x)=2x^3+5x^2-83x+40=arrow_forwardFind the Maclaurin’s polynomial of degree 3 for ( a ) f ( x ) = (1 + x ) e 2 x ( b ) f (x) = ln(3 + ex )arrow_forward1. Construct interpolating polynomials P1(x), P2(x), and P3(x) of degrees 1, 2, and 3 respectively using Newton's forward difference formula. x f(x) 8.1 16.94410 8.3 17.56492 8.6 18.50515 8.7 18.82091 2. Approximate the value at x=8.4 using each of the polynomials obtainedarrow_forward
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