Abstract Algebra: Let p(x) = 2x3 −3x2 + 4x−5 and q(x) = 7x3 + 33x−4 in R[x], where R = Z/3Z. Compute p(x) + q(x) and p(x)q(x).

Q: 9. What is the antiderivative of f(x) = 6x² – ? 2 а. 12x + x2 b. 3x³ + x2 e 3x3 - x2 d. 3x3 – 2 In x…

A:

Q: 16 Therefore f(x) = = co + C1x + c2x²+.. , where %3D x2 + 2x – 3 Co = C¡ = C2 = C3 =

A: given a function : f(x)=16x2+2x-3 We need to obtain it in the form of : c0+c1 x+c2 x2 + ... where c0…

Q: Q3) If f(x, y²) = x² + y² + vxy find af(x².y) and (x²y) ax ду

A:

Q: (B) Find the solution of f(z) = x'+6x'y+i 3x'y by using Cauchy-Riemann method

A: we have to solve the given problem

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = (x2 + y2 + z2)-1/2

A: Differentiating with respect to x, keeping y and z as constants, we get

Q: x = c e + c2t e“ O x"- 36x'+ 12x 0 6. O x"- 12x' + 36x = 0 %3D O x"+ 12x'- 36x = 0 O x" - 4x'+ 9x =…

A: for a differential equation having repeated roots m of auxillary equation thenthe solution or the…

Q: Find the orthogonal trajectories of the family of x² – y² = A. y? = x² + c B. xy = c C. y(6x² – y²)…

A:

Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: Find a general solution of y"- 2iy'+3y= 0.

A:

Q: Find (e3x + 5sinx)dx. -e3x +5cosx +C O a. 3 e3x+1 -5cosx + C b. 3x + 1 e3x -5 cosx + C OC. -e3x -…

A:

Q: Find the two conditions on b1, b2, and bz which determine solvability of 4 8. 3 4 =6= b2 -6 -7 -8 b3

A: The objective is to form the equation involving b1, b2, and b3 that determine the solvability of the…

Q: Find the linearization of y = eV3x at x = 64. %3D (Use symbolic notation and fractions where…

A:

Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

A:

Q: 2=Cメて+x -x2 Using Cramer's Rule メメt10n- 3xx=5 %3D

A: Solution using Cramer's rule is given as follows :

Q: le followihg s x + 2y = -2 -3x + 2y = -10 %3D %3D

A: To solve for x and y

Q: (e) f(x1,x2) = xỉ/x2 on R x R++.

A: The solution of (e) is in below

Q: (c) f(x) = e² – x + In(x) %3D

A:

Q: iii) ä(t) – 9x(t) = 0, x(0) = 1, ±(0) = 0 -

A:

Q: 2- X-J =(M(404) 3x उ्रुफट (X) %3D gu) =x°-8e

A:

Q: f(z) = 2(x – 5)² + 3. - f (x) is invertible for which values of x?

A: Given function is: fx=2x-52+3 Then we get,…

Q: The integraing factor of (4xy+3y²–x) dx+x(x+2y) dy= 0 is A x² B c) 2x-2 D 2x-1

A:

Q: r²[(x²-y²)²] 1²₂5²² du dt x+y

A:

Q: 1 of f(z): is z2+2z+2 %3D

A:

Q: af If 2xy(-x² + y) + xe", what is ду ду? Select one: а. 4ху — 2x3 + хеУ ду? 2x(-x² + 1) + xe" b. ду?…

A: Given ∂f∂y=2xy−x2+y+xey

Q: What is r' (x) when r(x) = In (x + 2x2 + 3x + 1)? %3D Select the correct answer below: O In (3x2 +…

A: Given: r(x)=lnx3+2x2+3x+1 We have to find the r'(x)

Q: 1. Use the Chain Rule to find y = (u-2)³ and u = da in terms of x. 1 2x+1

A:

Q: For Exercise, find the partial fraction decomposition for the given rational expression. Use the…

A:

Q: From the given equation below, compute x1X2, and X3 using LU decomposition. X1 — 3x2 + Xз 15 ЗX1 +…

A:

Q: Find the su x² + y? :

A: The surface is given as z=xy. Take the derivative of the surface, z=xyfx=y, fy=x. The surface area…

Q: Find the general antiderivative of f(x) = = + C -28²³-03-2/3 + √²

A:

Q: Your major online bookstore is in direct competition with Amazon.com, BN.com, and BooksAMillion.com.…

A: Algebra Question

Q: Exercise 0.2.12: Is there a solution to y' = y, such that y(0) = y(1)?

A:

Q: -3 Show that y(x) = -9x7 is a solution to 4x²y" + 12xy' + 3y = 0 for x > 0. %3D

A: We will show in step 2.

Q: 11. Eliminate the arbitrary constants of cx? + x + y² = 0.

A:

Q: Find the linearization at x = a. y=(14 + x) 12, a = 1 (Use symbolic notation and fractions where…

A:

Q: Q3. Integrate (x-1)(r+1)

A: To find the integration

Q: Show whether the two equations y₁ = using the Wronskian. 12e and y2 1.2e are independent or…

A:

Q: 190.19 b.) 6Xi t 15X2-24 y3 f 40x4 > 69.8 ¥3 15X, + 9x2 -13 V3 -24Y1 参3X t18 y3- 1 Xy = -163 " xy=…

A: Here we use a = x1 b = x2 c = x3 d = x4

Q: 2x4 - 3x2 - 12x + 6 at 0 and -2 to deter f(x) = ero exists between the two values.

A: we have to evaluate the f(x)=2x4-3x2-12x+6 at x=0 and x=-2and to determine if the intermidiate value…

Q: 7] The Wronskian of the functions 1, x, and e -2x is (а) е' -2x (2x+1) (b) 4e-2x (c) -e(2x +1) (d)…

A:

Q: The solution for the IVP: -00 %3D u(x, 0) = 2 x u(x, 0) = -e-x O a u(x, t) =x+ -(x+21)-e-(x-20) 4 O…

A: Known fact: For the system, utt=c2 uxx,   -∞<x<∞, t>0ux, 0=fxutx, 0=gx The D-Alembert's…

Q: T: P2 P2, .2 T(ax2 + bx + c) = ax² + bx +c B = {1, 1 – x, (1 - x)²} B' = {1, x , x²} v = x² – 3x +3…

A:

Q: af 8. Find and ax of f(x, y) = e-* sin (x + y) ду

A: A detailed solution is given below.

Q: I need help checking my answers. Thank you for your help.

A:

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

A:

Q: Your major online bookstore is in direct competition with Amazon.com, BN.com, and BooksAMillion.com.…

A:

Q: Find the linearization of y = (1 + 9x)-12 at x = 7. (Use symbolic notation and fractions where…

A: Given, y=1+9x-12 Linearization is given by, L(x)=f(a)+f'(a)(x-a) Assume f(x)=y=1+9x-12 Differentiate…

Q: 3a Show that the method xn+1 = Xn 6+ Xn ,converage to vā. %3D a

A: