(a) Is the polynomial 1 + 2x − xª¹ € Z₁[x] irreducible over Z₁? Justify your answer.

Q: Prove that the function f(x) = sin r x¹/3 is absolutely Riemann integrable over [0, 1].

A:

Q: Several friends chartered a boat for a day's fishing. They caught a total of 67 fish. The table…

A: We will determine the empirical probability that the next fish caught is a kingfish. From the given…

Q: The drug concentration in the bloodstreams t hours after injection en mately by C-5.450s155, where…

A:

Q: Which one of the following is an equation of the line through points P(1,-1, 2, 1) and Q(3, 1,…

A: We have to find an equation of the line passing through points P(1,-1,2,1) and Q((3,1,1,-1)

Q: Write the matrix A = []→³ representing B- the input and output bases are both B. Write a basis for…

A:

Q: (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2)…

A:

Q: (2n+1)! ο Ση=1 (3)η

A:

Q: Find the power series solution about x = 0 : dy 2x + dx - y dx² - 2y = 0.

A:

Q: c) Σ=1(−1)nn3 3η

A:

Q: 3. Consider the set X = {a,b,c} and the function f: X→ X defined by the rules f(a) = b. f (b) = a…

A: The set X=a, b, c and the function f:X→X defined by the rules fa=b, fb=a, fc=b. We have to find the…

Q: If p, q are positive integers, fi defined for positive numbers only positive values such tha p.y^q…

A:

Q: Q1) solve the system Ax=b by using LU factorization. A= [8 8 6 3] [3 1 7 1] [7 6 7 4] [9 6 1 8]…

A: We solve given system by LU decomposition.

Q: Question 2: Given the function f(x, y) = sin(x + y), at the point P(π/3, π/4), What unit direction…

A:

Q: Question 1: What are the directional derivatives of the following functions along the given…

A:

Q: 2. Use Fermat's method to find the general sub-tangent and tangent to the curve whose equation is…

A:

Q: 41. Future Value $15,000 is deposited for 4 years in an account earning 8% interest. a. Calculate…

A: Solution :-

Q: a) Verify Green's theorem in the plane for f(3x² - 8y²) dx + (4y - 6xy) dy, where C is the boundary…

A:

Q: • f(x, y, z)= . near the point (1, 1,0).

A:

Q: Prove that if lim f(x) is of the form X4x g(x) Write a 8- & proof. then lim f(x) g(x) X1x -0. =

A:

Q: Find the Moments (Mx) for the lamina that occupies the region D and has the given "Density" function…

A:

Q: 3. (Dual of Linear Program with Inequality Constraints) Find the dual problem (including the…

A: Find the dual of the linear program with inequality constraints. minimize cTxsubject to Ax-b≤0 This…

Q: coordinates of the center of gravity of the upper half of the circle: Find the x² + y² = a²

A:

Q: Prove that F(x, y, z) = (y 2 cos x+z 3

A: Introduction: A vector field of the form F(x,y,z)=f (i)+g (j)+h (k) is a conservative field when it…

Q: Approximate ff(y-x²+2) dA for R= [0, 2] × [0, 3] using n = 4 subintervals in th R x-direction and m=…

A: Introduction: A basic calculus strategy is to start by providing an approximation for a given issue,…

Q: At graduation, you have a student loan of $20,000. The loan has a fixed annual interest rate of…

A: Now the monthly payments when the loan amount is P taken for n months at a rate of r% is…

Q: (b) If F(x, y, z)=zzi+3ayj-22k, evaluate J, F-dS using Gauss's theorem when S is the closed cylinder…

A:

Q: Question Three (a) Prove that F(x, y, z) = (y² cos1+=³)i+(2y sin x−4)j+(3zz+2)k is a conservative…

A:

Q: The function f(x) = x³ - 6ax² + 5x satisfies the conditions of Lagrange's mean value theorem over…

A:

Q: The graph of f(y) is given below. Use it to answer the following. Let y' (t) = f(y). Identify the W…

A:

Q: 1. Find the Fourier cosine series of the function f(x) given by if 0<x< 2; 4-x, if 2 ≤ x < 8 and…

A:

Q: SSSRf(x,y,z)dxdydz

A: To Express: The triple integral ∫∫∫Rf(x,y,z)dV  where R is the solid bounded by the curves y=x2 ,…

Q: (a) Let U = 3i -j – 4k and V = −2i+ 4j - 3k. Show that U - V is commutative but UX V is not. (b) For…

A: Introduction: Since vector addition adheres to the commutative property, the order of addition is…

Q: Investigate for maxima and minima the function ƒ(x)=[{2(t−1)(t−2)² + (x − 1)² (t−2)²}dt

A:

Q: Let u, v ER" be two linearly independent vectors let A = u. v be their outer product. What is the…

A:

Q: Use the union rule to answer. If n(A) = 6, n(B) = 11 and n(An B) = 5, what is n(A U B)? n(A U B) =

A:

Q: Problem 1: Use an LU-factorization of the coefficient matrix to solve the linear system 2x1 -2x1 +…

A: Write the given system of equations in matrix form, that is, in the form AX=B.…

Q: Question 1. T = T, #, *> is a ring. Given that S = S, +, > is a ring with unity e, and (a) The…

A:

Q: Use the basic building block = Σa", |z| < 1, together with the properties stated in n=0 this section…

A:

Q: Solve B. V. P Ut = kuxx, -∞ 0 u (x,0) = e¯|x| By using Fourier integral

A:

Q: If the area of the triangle included between the axes and any tangent to the curve x^ n * y = a ^ n…

A: Given that, The area of the triangle included between the axes and any tangent to the curve xny=an…

Q: At what point (x, y) is the function f(x) = -8x - 8 closest to the point (1, −6)? Enter an exact…

A:

Q: For the following integral, reverse the order of integration and evaluate the integral. 1/4 1/2 SS…

A:

Q: The revenue equation (in hundreds of millions of dollars) for barley production in a certain country…

A: Given that the revenue equation (in hundreds of millions of dollars) for barley production in a…

Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

A: Given: limn→∞ 6n2-2n412n3+2n2-17n   Property (i) limn→∞f(x)g(x)=limn→∞ f(x)limn→∞ g(x)    ,…

Q: Let a1, b₁, a2, b₂ € N. Prove the following: If a₁ +b₁√√2 = a2 + b₂√√/2, then a₁ = 02 and b₁ = b₂.…

A:

Q: Using the definitions of limit and/or infinite limit, show that if limn→∞sn = ∞, then also…

A:

Q: Find the Moments (My) for the lamina that occupies the region D and has the given "Density" function…

A:

Q: Find the mass and the center of mass of the following solid: The tetrahedron bounded by the planes…

A: The given problem is to find mass and center of mass of the given solid tetrahedron bounded by given…

Q: In the following list, select all the correct expressions if G(x) is the generating function of the…

A:

Q: I Let f: RR be the function defined by f(x) || if x = 0, and f(0) = a. Is there a choice of a so…

A: