Evaluate the following integrals using (a) Trapezoidal Rule and (b) Simpson Rule by finding n such that error is less than 10-6, T/2 1. f/²(1 + 2 cos x) dx

Q: Q3) Find the minimum of the Brown's badly scaled function using Powell's method. f(x) = (x₁ - 106)²…

A: We will use the basic knowledge of partial derivatives and differential calculus to answer this…

Q: X (3+x) 1-x (2-x 4+x) 2 -10 5 -X ܝ 48

A:

Q: 11. The equation of a sphere with center at (-3, 2, 4) and of radius 6 units is? a. x² + y² + z²…

A:

Q: Determine the value/s of D if the graph of the equation x² + 4y² + Dx - 4y + 2 = 0 a. is an ellipse;…

A:

Q: 12. Show that the set of all constant polynomials in Z[r] is a subring but not an ideal of Z[x]

A:

Q: Determine the value/s of D if the graph of the equation x² + 4y² + Dx - 4y + 2 = 0 a. is an ellipse;…

A:

Q: Let I be the set of real numbers equipped with the standard topology. Let A and B be two subsets of…

A:

Q: Consider the following ODE: dy 2xy = y² sin(x) + x² cos(y) dx With y(20) = 1.6 for 20 ≤ x ≤ 70. A.…

A: %%ode45 clear all % y1=(y*sin(x)/(2*x))+(x*cos(y)/(2*y)); tspan = [20 70]; y0 = 1.6; [x,y] =…

Q: 1. What number when divided by 2,5,7,11 and 17 you'll get -17,-11, -7,-5 and -2 respective…

A: Note: According to our guidelines we can answer only first question

Q: 3. In the last homework assignment, you computed the volume of the solid obtained by rotating the…

A: We will use the basic knowledge of integral calculus to answer this question correctly and…

Q: lowing Vectors Linearly Dependent 1,438) ₂ (3₁-330) Ans. Dependent

A:

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y) =…

A: Solution

Q: WHAT is this type of circuit or graph a. Hamiltonian circuit b.Euler path c.Hamiltonian path d.Euler…

A:

Q: Q.5. D.] find the Cartesian equation of the plane r(u, v) (u,v + 2,3u-2v), -1≤u≤2 and -2≤0≤3

A: To find the cartesian equation of the plane from a given parametric equation, we need to eliminate…

Q: 4-In any elements is the only hilpolent elements ) a(-b) = (-a)b = - (ab) (ii) 1) (-a) (-b) = ab

A: To prove:(a) a-b=-ab=-ab              (b) -a-b=ab

Q: There was no final solution

A:

Q: n+1 2n + 1 5+8n² (b) t = 2-7n² (c) t₁ = (-1)" (1₂2) n+2) (a) t₁ =

A:

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

A:

Q: t, f(t) = 2t - 1, 0, 0 < t < 1 0<t<2 otherwise

A:

Q: Suppose the average costs of a mining operation depend on the number of machines used, and average…

A:

Q: 4) By using Newton's backward formula for the derivative, find f (0-9) + f (0-9) 6 1 (0-8) f(0.8) N…

A: We first make backward difference table: x y=f ∇y ∇2y ∇3y ∇4y 0 0             0.12-0=0.12…

Q: Find the Fourier Transform of Sel2t -1<t<1 f(t) = {e1²t 0 elsewhere

A:

Q: 1. Find the general solution of 2 ylnx dx = (x+¹) ²

A:

Q: (3x+2) XP Xso E 2 хр пр., ха 1500 X_s t

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use Laplace transform to obtain the output current i(t) in ampere for t = 1 second for the given…

A:

Q: olve the differential equation y'(t) - 2y(t) = e2t; y(0) = 1.3. Vhat is the value when t = 1.20?…

A:

Q: A. Find the general equation of the conic with the given properties. 51 1. A parabola with directrix…

A: Let us consider the general equation of  upward or downward parabola (x-h)2=4p(y-k) Focus is (h,…

Q: Test the convergence of the following: n 3n+1 1- an 3n-1 2 (n(~²+1))" n=1 2- =

A:

Q: How many integers between 1 and 822 inclusive are divisible by 5 or 3?

A:

Q: For each angle in standard position, find a coterminal angle 8, where 0° < 0 < 360°. After which,…

A: We know that if we add or subtract integral multiple of 360° in any angle then we will get it's…

Q: Consider the vector field Ĥ(x, y, z) = (y², x, z²). Let S3 be the portion of the paraboloid 2 = x² +…

A:

Q: Determine the value of 'k' if the L[ tk4t ] = 1/(s² - bs + 10).

A:

Q: Consider xy' = y(lnx - Iny) with y(1) = 4. Using Runge-Kutta method with h=0.1, the k₁ in the…

A: The given O.D.E is xy'=ylnx-lny with y1=4. To find: the value of A.

Q: 10 5-2 sin 8 a. find the eccentricity and identify the type of conic; b. write an equation of the…

A:

Q: 2 ecos cos(send) 0 5-4 cos(6) Jo -do = 2π € 500 cos cos(sen)

A: We have to use the integral of the solution of the Dirichlet problem on the disk of radius r to…

Q: Write the formal negation of the following statement: ∀ n ∈ N, ∃ x ∈ R s.t. x < 1/n

A:

Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

A:

Q: If w is a vector such that w+(ŵ×ü) = v,then prove that only if u is perpendicular to v.

A:

Q: 2. Find the center of mass of the lamina in Exercise 11 if the density at any point is proportional…

A:

Q: 2. Determine the Fourier series for F(x) = -2 when F(x) = 2 when -π<x<0 0<x<T

A:

Q: Approximate the integral of f(x) = x² - 2x + 4 with the following unequally spaced points shown in…

A:

Q: Find the closest line to the points (1,4.5), (3, 4.5), and (4,1). Identify the following components:…

A:

Q: Solve for x: | cosx-2 sin 2x-cos 3x|=1-2 sin x-cos 2x

A:

Q: Consider xy' = y(lnx-lny) with y(1) = 4. Using Runge-Kutta method with h=0.1, the k² in the…

A: given equation  xy'=ylnx-lny with initial conditions y1=4 using Runge Kutta method with h=0.1 , the…

Q: -a+b+c b The linear transformation L: R4 → R³ is given as L (0)-[] b с 2a-b a. Determine the matrix…

A: (a) If Tx=Ax, then A is called matrix of linear transformation. (b) λ is called eigen value of a…

Q: By using Laplace transform to solve y" + 4y + 8y = sint with y (0) = 1 and y' (0) = 0, what would be…

A:

Q: Suppose the slope of the tangent line at any point on a curve is curve passes thru (1,3),…

A: We will find approximate value of y at required point  and then find  slope of tangent line . Using…

Q: Solve each of the following by Laplace Transform: 1.) ď² y +2 + Y dy dt - = sinh 3t - 5 cosh 3t dt²…

A:

Q: A budgle with a PCV of 45% presented to the clinic. A diagnostic laboratory requires 1 ml of serum…

A:

Q: Find the range, mean or average deviation, variance and standard deviation of the following grouped…

A: