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...
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.
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...
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)?...
The output of the system if not given assume output is initially z vin) 5x[n]-4x[n-1]+3x[n-2]-2x[n-3]+x[n-4] zero to the input x[n) Stn]+ 5n-1] Hint: several methods for solving this : superposition, direct substitution, and convoultion O vin]=[5 1 1 11 1] O vini= 3-2 10] 4 o inl-10 5 4 3-2 1 O in1-(5 9 7531] The output of the system if not given assume output is initially z vin) 5x[n]-4x[n-1]+3x[n-2]-2x[n-3]+x[n-4] zero to the input x[n) Stn]+ 5n-1] Hint: several methods...
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)...
1.) (12 pts.) Consider the vector field F(x, y, z) = (3x” 2 + 3 + yzbi – (22 - 1z)] + (23 – 2yz + 2 + xy). Find a scalar function f, which has a gradient vector equal to F, or determine that this is impossible,
3x + 4 for x 2 12. Let (x) 2-x for -1 <x51 . Find f(1/3) and (3/2). Sketch the graph of the -3x for x S-1 function. Determine the domain and range. (2,2,5, 3, and 3 points)
Question 20 1 pt 31 Details Let f(x) = (3x + 2) (4x - 3)(x +9) Find the domain in interval notation Note: Use -oo for -00,oo for oo, U for union. Submit and End
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.