Calculate sin x So √1+x with an estimate error less than 10-6, using Romberg's integration? -dx.

Q: Let a be the positive real fourth root of 3. Factor the polynomial x¹-3 into irreducible factors in…

A:

Q: Consider the Boundary-Value Problem: ² ²u 9 = dx² 000 a(0, 1) = 0, u (2, 1) = 0,05155 u(x, 0) = 3x…

A:

Q: Suppose that E is the splitting field for some polynomial over GF(p).If Gal(E/GF(p)) = p6, how many…

A: Given: E is the splitting field for some polynomials over GF(p). And Gal(E/GF(p)) = p6. We have to…

Q: Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C². 45 -54…

A: Given, The matrix A = 45-54   We have to find the eigen values and eigenspaces.

Q: Consider the sturm-Liouville Problem d²p dx² for oexal, with boundary condition +x=0 $(0) - do (0)=0…

A:

Q: 7. Find the area of the region enclosed by r = 2 cos 0 and r = 2 sin 0. (Find graph from book). 8.…

A:

Q: Evaluate the following integrals using contour integration ( 1 -dx 13+5sinx

A: A line integral is used to find the integral over a complex plane. The path of line integral is of…

Q: 7x/4 Evaluate the integral (sinx + cos x) dx using the fundamental -x/4 theorem of calculus. Discuss…

A: The given integral is, fx=∫-π/47π/4sinx+cosxdx. To Evaluate: The above integral. Also,  To Explain:…

Q: In each of Problems 14 through 20, find all eigenvalues and eigenvectors of the given matrix. 5 3 3…

A:

Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

A:

Q: Let V be the group of vectors in the plane, with vector addition as the binary operation. Show that…

A:

Q: Minimize z = 3x + 4y subject to the constraints   3x - 4y ≤ 12, x + 2y ≥ 4   x ≥ 1, y ≥ 0.

A: Solution :- While solving problems , it is considered as x=x1 & y = x2 Problem is Max Z =…

Q: For Questions 10-13: While running for city council, Erika plans to hand out fliers to every house…

A:

Q: What's the numerical approximation to the integral c COS Type your answer... √xdx? Use trapezoidal…

A: Trapezoidal rule

Q: Problem 4. Given a scalar a, the exponential eº can be expanded by Taylor series as: (b) eª 1 =1+a+…

A: Given: A=111010012 and A is diagonalizable. To Do: (a) Express eA by eD. (b) Compute eA.

Q: Which of the following are true regarding the first derivative of the function f(x) = cos √x at x =…

A: Given: Function fx=cosx is given. To Find: One needs to evaluate the first derivative using forward…

Q: Use a graphing calculator to find the first 10 terms of the sequence an its 9th term is its 10th…

A:

Q: Let f: (– 2,2) → R be defined by f(x) = (n+ 1)_x". Find Σ n=0 2⁰ 1 f f(x) -1 f(x) dx

A: Given:f : -2, 2 → ℝ is defined by: fx=∑n=0∞n+12nxn To Find: ∫-11fxdx.

Q: A vector in the direction of vector i -23 + 2k that has magnitude 15 is î-2j + 2k 3 O 5 -10 + 10k O…

A:

Q: For each series, determine whether it converges absolutely, converges conditionally, or diverges. ∞…

A: Test for absolute converges

Q: 2 A circular wire hoop of constant density 8 = 2 lies along the circle x² + y² = 8a² in the…

A: Given: The density of the circular wire hoop is δ=2, and it lies along the circle x2+y2=8a2 in the…

Q: 1- How many roots does each of the following equations has? a- Cos x=e* b- e*= 1+ Sin x c- Inx=x² d-…

A:

Q: Let B be the standard basis of the space P2 of polynomials.Use coordinate vectors to test whether…

A:

Q: f(x, y) = x² - 9xy + y² + 7y+1

A: Find the saddle points for both functions below. Enter each point as an ordered triple, e.g.,…

Q: Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T…

A:

Q: please provide the correct answer

A:

Q: change order of integration to dydzdx 1 x+2 3-y [ ] [ f(x, y, z)dzdydæ -1 x²

A:

Q: Evaluate the surface integral. 11. ³² ds. y² dS, S is the part of the sphere x² + y² + z² = 1 that…

A:

Q: Find a particular solution for y" - 4y - 12y = x using the Method of Undetermined coefficients.

A: Solution :- y'' -4y' -12y=xA second order linear, non-homogeneous ODE has the form of…

Q: Compute the integral $12)=3/2 (2¹0 + 1)(2+2+1) (z¹2 i) dz

A:

Q: Solve the equation y'' + xy' + 2y = 0 near x = 0 using the power series method. Each of your series…

A: Sol:- y'' +xy' +2y=0A linear homogeneous ODE with constant coefficients has the form of pxy'' +qxy'…

Q: Find a unit normal vector of the surface at the given point P. x² + y² = 25, P: (4, 3,6)

A: The equation is x2+y2=25 and the point is P4, 3, 6. Now, the unit normal vector is n^=∇ϕ∇ϕ. Now, for…

Q: Write down two unique non-zero vectors à and b in the 5th dimension, R5 (no entry should be 0). a.…

A: The main objective is write two non zero vectors in ℝ5. Find the given values.

Q: A 160-lb person who runs at 8 mph for 1 hr burns about 840 calories. The same person, walking at 2…

A: 160-lb person who runs at 8 mph for 1 hr burns about 840 calories.Hence at 8 mph in 1 min he burns…

Q: aw Find when u = 0, v = 0 if w = x² + ₁ x Əv Əw Əv I 0 x-0 x=3u-6v + 1, y = 3u+v-2. (Simplify your…

A: Here, w is a function of x and y. Again, x and y are functions of u and v. By chain rule, we have,…

Q: - The helix curve is (d) Find the torsion 7. 3 a(t) = (cost, sint, 2). 2 (e) Find the curvature k.

A:

Q: We want to use the Alternating Series Test to determine if the series: k² √k6 +3 k=4 (−1)k+2_…

A:

Q: x"+ 2x'+ 5x = - - 20 8(1-2) Initial Conditions: x (0) = 10, x'(0) = -2 8 = the Dirac Delta function…

A: The given problem is to solve the given initial value problem with initial conditions and also to…

Q: 3. Reduce each of the following to the smallest non-negative residual. (a) 87122 mod 23 (b) -7823…

A:

Q: (a) Compute V × F · dŜ where F(x, y, z) = (z − y, x, −x) and S is the hemisphere x² + y² + x² = 4, z…

A:

Q: Consider the function f(x) = = −1, X, 1, −2 < x < −1, −1 ≤ x < 1, 1 ≤ x < 2. (a) Sketch the graph of…

A: Graph of the function and it's series

Q: (A) B D (E) Given the differential equation: (x-2)y' +y=0 y(x) =c, Σ (2x)" 0 n=0 The recurrence…

A:

Q: · Let S : RCUN) = < u² Losv, u²³-4, 4²-sinv), (u₁v) & [13] x [2₁4] Evamate : do (y+4)³2 SS S

A: Note: For r→(u,v)=&lt;x(u,v), y(u,v), z(u,v)&gt; , take dσ=||ru→×rv|→|dA

Q: -Please make sure to show step by step what you have done when solving the problem. For the…

A:

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t)= 0-30 A=…

A: Here, we use eigenvalues and eigenvector method to find solution.

Q: Consider the following matrix: 30-8 -4 03 8 4 0 0 11 4 0 0-24 -9 A= a) Find the distinct eigenvalues…

A: Diagonalization of the matrix

Q: 3) A cylindrical hole is drilled along diameter of a sphere w/ radius R. Tk rady of the cylinder is…

A:

Q: Find all limit cycles of system x₁ =−x₂ + x₁(1-x² - x²) (2 - x² - x²), x₂ = X₁ + X₂(1 − x² − x²)(2 −…

A: As per the system we are given a 2d nonlinear dynamic system and we have to find : The limit cycles…

Q: A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A. A…

A:

Q: Prove the following for any given sets A, B, C and D. 3. ACB iff P(A) CP(B). 4. ACB if and only if…

A: Let P(A) denotes the power set of set A, that contains all the subsets of set A.