Please see the attached file for the fully formatted problems. 1. ? Calculate the Taylor Polynomial and the Taylor residual for the function . ? Prove that as , for all . ? Find the Taylor series of f. ? What is the radius of convergence for the Taylor series? Justify your answer. 2. ? Let f:[0,1] be a bo
From the given polynomials, identify the polynomials of degree one. a. 311y - 5 - 43y b. (11y2)1/4 + 14 c. 10 + 19x - 2x2 d. 2 + 15x e. 52y4 + 7x + 2 f. (68)1y1 g. x3 + 3x - 9 Solve the following: i. -2x = 3x + 4 ii. 3x/4 = 6 iii. y/6 + 1 = 9 iv. 6 = -2x/4 v. Find f(1) for f(x) = 4x3 - 3x2 - x + 2
A. Solve the following questions involving fundamental operations on polynomials a.Find p(x) + 4q(x) given p(x)=4x4 + 10x3 - 2x2 + 13 and q(x) = 2x4+ 5x2 - 3 b. Find P(-1/2) if P(x) = 2x4 + x3 + 12 c. Simplify: (-4 + x2 + 2x3) - (-6 - x + 3x3) - (-6y3 + y2) d. Add: (2x2 + 6y2 + 4z2 + 3xy + yz + zx) + (4x2 + 3y2
Please see attached document. There are four problems. The first problem is 71! mod 73
For this problem it helps to know that: 3x7x13 = 273 (a) Define the Euler Totient function, (SYMBOL) For (b) to (f) please see attached. (PLEASE SEE ATTACHMENT FOR COMPLETE PROBLEM AND PROPER SYMBOLS)
1. (a) Use the Euclidcan Algorithm to find the greatest common divisor of 13 and 21 (b) Is 13 invertible in Z21? If so, find the reciprocal. (c) Suppose x and yare integers, what is the minimum positive value for 13x+21y? Determine all posible values of (x,y) for which the minimum is obtained. (PLEASE SEE ATTACHMENT FOR
Factor into primes the following positive integers: (a) 25 (b) 4200 (c) 10(to the exponent)10 (d) 19 (e) 1 *Please see attachment for proper citation and complete instructions
Find two numbers that have a product of 81 and also have a sum of 30 (use prime factorization for the product) Please see attachment for the formatted question.
Perform the indicated operation ... (see attachment)
Ace manufacturing has determined that the Cost of Labor for producing x transmissions is: 0.3x(squared) + 400x+550 dollars While the Cost of Materials is: 0.1x(squared) + 50x+800 dollars · Write a polynomial that represents the total cost of Materilas and Labor for producing x transmissions. · Evaluate the total cost pol
Given A=(-1/2+isqrt(3)/2)^n 1. Show that A is real for any natural n 2. Show that for n=3K where K is a natural number, A=2
1. The equation X^5 - 2X^4 - X^3 + 6X - 4 = 0 has a repeated root at X=1 and a root at X-2. By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of X^5 - 2X^4 - X^3 + 6X - 4 2. Given that cosX= (e^jx + e^-jx)/2
F(x) = ln5 + ln(1-1/5x) Using substitution in one of the standard Taylor series, find the Taylor series about f for 0. Give all terms up to the term in x^3.
See attached file for full problem description. (a) Prove that if g.c.d.(n,p) = 1,then p divides n^(p-1) -1. (b) Prove that if 3 is not a divisor of n, then 3 divides n^2 -1. (c) Pr
In the two-player game of Two Stacks, a deck of cards (with the joker added, for a total of 53 cards) is randomly divided into two piles. The two players take turns removing cards from one pile or the other. On a player's turn, that player may remove any positive number of cards from a single pile. The object of the game is to r
I am having trouble with the following problems. Can someone please help me and explain the process? P. 295 1. # 16 2. # 28 3. # 36 P.309 4. # 78 5. # 80 6. # 82 P.334 7. #28 8 #44 P.364 9. # 36 10. # 46(Use Grapher only) See the attached file.
Problem: Let f(x) and g(x) be nonzero polynomials in R[x] and assume that the leading coefficient of one of them is a unit. Show that f(x)g(x) doesn't equal 0 and that deg[f(x)g(x)] = deg(f(x)) + deg(g(x))
The problem is attached. Express x^8 + 98x^4y^4 + y^8 as a product of two polynomials of smaller degree with integer coefficients.
Find all the integers such that when the final digit is deleted the new integer divides the original one. Can you generalize this to deleting other digits?
Decipher the following CFQGE KAZEMF ZMAGVMC NMO VYSV which was obtained by a formula of the type y=kx (mod 26)
A. Find 12/25 divide by 1/5 in two different ways. Explain your methods. b. Explain, using a diagram, how the following problems illustrate the two interpretations of division: partitive division ans measurement division. i. A road crew repaves 1 1/2 miles of road each day. How long will it take the crew to pave a 3/4 mile
Rewrite in the simplest form. State the GCF(greatest common factor) of numerator and denominator in each case. 1. 34/85 2. 123123/567567 Find 5/9+7/12 using three different denominators. Give your answers as mixed numbers in lowest terms. State the LCM (least common multiple)of the denominators.
Prove that if p is a prime number, then p divides , for all n≥p. Here [r] denotes the greatest integer ≤ r , for any real number r. Does this result generalize to a result about instead of p ?
Show that z and iz have the same modulus. How are the graphs of these two numbers related?
If m =/ 0, then (m4)/m4 = a)1 b)m2 c)m4 d)m12 e)m16
For a mapping %:A -> B, let == denote the kernel equivalence of %, and let *:A -> A== denote the natural mapping. Define $:A== -> B by $([a]) = %(a) for every equivalence class [a] in A==. 1. Show that $ is well defined and one-to-one, and that $ is onto if % is onto. Furthermore, show that % = $*, so that % is the composite
Given ( INTEGRAL ln square(x)dx, as x from n to n+1 ) = ( INTEGRAL ln square (n+x)dx, as x from 0 to 1 ) = ( INTEGRAL [[ln(n+x) - ln(x) + ln(n)]square] dx, as x from 0 to 1 ), (a) Verify that ( LIMIT (n/ln(n)) [INTEGRAL (ln square (x)dx) - (ln square (n))] as n approach to the infinity ) = 1 (b) Compute LIMIT ((n square)/
Here is what the problem asks for: Give an example of a polynomial function f of degree 5 such that the only real roots of f(x) are -2,1,6 and f(2)=32. Show that your example works and leave f(x) in factored form.
Note:% just a symbol Let I be an open interval containing the point x.(x not), and suppose that the function f:I->R has a continuous third derivative with f'''(x)>0 for all x in I. Prove that if x.+h is in I, there is a unique number % = %(h) in the interval (0,1) such that f(x.+h) = f(x.) + f'(x.)h + f"(x.+%h)(h^2)/2