1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why.
2- What is the analogy between Z and F[x]?
3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x].
(a) Perform the following computation in Z5[x]/(p(x)). Give your answers in the form [r(x)] where r(x) has degree as small as possible.
i. [4x] + [3x^2 + x + 2]
ii. [x^2][2x^2+1]
(b) Show that Z5[x]/((p(x)) has zero divisors.
1- What are the units in Z? What are the units in F[x]? Don’t write out a formal proof, but discuss why. 2- What is the analogy between Z and F[x]? 3- Let p(x) = x^3 + 3x + 1 = (x+3)^2 * (x+4) in Z5[x...
Let f(x)= -3x^4+79x^2-3x+1/ 5x^4+19x^3+2x+5. Discuss the short run behavior for f(x) and the long run behavior for f(x).
Which function below is the inverse of f:R-{2} → R-{3} ut of f(x)= -3x+1 X X-2 Select one: O a. f-1: R-{3} → R-{2} f'(x)=2x+1 X-3 O b. f-1: R - {2} → R-{3} F"(x) = 2X+1 X-3 f-:R-{2} → R-{3} f(x)= x-2 3x + 1 O d. f-1: R - {3} → R-{2} ... X-2 hook....pdf - POS Week 171 ..hantal ob. F-R-{2} → R-{3} F-1(x)=2x+1 3 F-1R- {2} → R - {3} X-2 pe d. f":R-{3} → R...
Let g: R→R be a polynomial function of even degree and let B={g(x)|x ∈R} be the range of g. Define g such that it has AT LEAST TWO TERMS G(x) - 1 - 3x^2 1. Using the properties and definitions of the real number system, and in particular the definition of supremum, construct a formal proof showing inf(B) exists OR explain why B does not have an supremum.
This problem is on Solving Systems of Equations In Three Variables (1) X-4y+3z=-27 2x+2y-3z=22 4z=-16 (2) 3x-2y+4z=15 x-y+z=3 x+4y-5z=0 (3) 2x+y-z=-8 4x-y+2x=5 -3x+y+2z=5
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
5,9,13,17 1-X 1. What is the difference between a Taylor series and Maclaurin series? 2. T/F: In general, pn() approximates f(x) better and better as n gets larger. 3. For some function f(x), the Maclaurin polynomial of degree 4 is pa(x) = 6 + 3x - 4x + 5x – 7x*. What is p2(x)? 4. For some function f(x), the Maclaurin polynomial of degree 4 is p(x) = 6 + 3x - 4x + 5x – 7x*. What is f"O)?...
4. Let 3 f(x, y, z) = x’yz-xyz3, 4 P(2, -1, 1), u =< 0, > 5 a). Find the gradient of f. b). Evaluate the gradient at the point P. c). Find the rate of change of f at the point of P in the direction of the vector u.
This is a MATLAB question so please answer them with MATLAB steps. Let f(z) = V3z sin(#) and P(z) =r-x-1. 1. Find f(e) 2. Find the real solution(s) to Px) 0. Hint: use the roots command. 3. Find the global minimum for f(x). Hint: plot f over [0,2] 4. Solve f()P. Hint: plot f and P over [0,21. 5. Find lim,→0+ f(x). Hint: make a vector hi make a table [x + h; f(x + h)]". 6. Find '(In 2)....
1 point) Match the functions below with their level surfaces at height 3 in the table at the right. 1. f(x,y,z) 22 3x 2.f(x,y,z) 2y +3x 3. f(x, y,z) 2y +3z -2 (You can drag the images to rotate them.) Enable Java to make this image Enable Java to make this image interactive] Enable Java to make this image Enable Java to make this image Enable Java to make this image Enable Java to make this image interactive] 1 point)...