For the IVP y' = 999e-t-1000y with y(0) = 1 would Forward or Backward Euler be a better choice for constructing a numerical approximation of y? Justify your selection. You don't need to carry out any computations but you might find them enlightening.

Q: Give the equations of all the asymptotes of the graph of f.

A: Given information is ∙ f is continuous everywhere except at x=2 ∙ f-1=-2,  f1 =0,  f3 =5 ∙ limx→2-…

Q: Suppose A is a 2 × 2 real matrix with an eigenvalue λ = 3 + 5i and corresponding eigenvector * =…

A:

Q: Determine in polar and Cartesian forms (a) [3/41°]* (b) (-2-)5.

A:

Q: g) y ext= cosh x + √cosh²x -1 +7 ex е X h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy dy -…

A:

Q: Approximate the following integrals using the following methods. ». [² [²√(x²y + x a. Composite…

A:

Q: 10. 1²+2²+...+ n² = n(n+1)(2n + 1) 6 integer n ≥ 1. s 12 for every

A:

Q: -x -e = luxe by Bisection Slove:.

A: To solve by using the bisection method.

Q: Problem 3 Given: Arg (Ln(z)) = 3 (radians) and |z| = 70. Find S Im(z) + Re(z) = Problem 4

A: Since ,we know that, Ln(z) = ln|z| + iArg(z+2n)Let us use the principal part of logarithm, i.e,…

Q: Calculate, to the nearest cent, the future value FV (in dollars) of an investment of $10,000 at the…

A:

Q: Resonance is not a phenomenon reserved for undamped mechanisms. Consider the model: d²x dr +2. +5.x…

A:

Q: Ques.4 Decomposition 3z = 14 Solve the system of three simultaneous linear equations by using Crout…

A:

Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sint + 7 cos t) k…

A: The given question is related with unit tangent vector. Given that,               rt = 7t cost - 7…

Q: Solve the given initial-value problem. 1 0 2 2 X'= X, X(0) = - (²) 1 X(t) = 1 -- 2

A:

Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: Suppose that f(x) and g(x) are given by the power series f(x) = 3 + 6x + 2x² + 2x³ +….. and g(x) =…

A:

Q: 1. Suppose that f(z) is analytic on 0 < |z| < ∞ and there exists a f(z) nonnegative integer m such…

A:

Q: Find the matrix A if 2e2t et e²t - et e2tet 2e2t - et 3e2t3et 3e2t-3et et-e2t et - e2t 3et - 2e²t

A: To determine the matrix A , firstly I have taken the derivative on both sides then putting t equal…

Q: Power Series 1 f(x)=√√2 + x about x = 1

A:

Q: Let fn, f be real functions on S2. Show ∞ ∞ ∞ {w: fn(w) + f(w)} = UNU {w: | fn(w) - f (w)| ≥ } }.…

A:

Q: Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit.…

A: Definition of the definite Integral

Q: 1. Draw the circuit corresponding to the following expression. (Do not simplify your expression or…

A:

Q: 18. Show that Σkind(k)³ = (Σk|n d(k))² for all positive integer n.

A:

Q: Round your answer to the nearest cent.) JHhUity account. HINT [See Quick Example 1 and Example 1.]…

A: Solution:-

Q: Compute the specified quantity. A 7 year bond costs $1,000 and will pay a total of $100 interest…

A: To determine the annual interest rate r for a 7 year bond costs $1000 and will pay a total of $100…

Q: . What is the coefficient of ?^4 when (3+4x^2)^3 is expanded?

A:

Q: as ủ = y. unit vecto . If the ve

A:

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: Let A=2-2703-20-12 We will find the characteristic equation and all eigenvalues (a basis for each of…

Q: 23 Find a 4 by 4 permutation matrix (call it A) that needs 3 row exchanges to reach the end of…

A: Consider the 4×4 matrix given below, A=0001100001000010 Here we need to apply 3 row exchanges to…

Q: -O 12-1₁ = 4 2 - 91₁ + 1 ₂ - 1 3 -9 14 = 0 8 3 I₁ + 10 I₂ + 7 13 -15 I4 = 100 Із -31₁ lo 1₂2 13 + 27…

A:

Q: please explain with a graph. Question 2. Let f: R R be defined by f(x) = x² - 4x 2. Show that f has…

A:

Q: Suppose that p≥ 5 is prime. Show that -3 is a quadratic residue (mo p) if p = 1 or 7 (mod 12) and a…

A:

Q: Suppose that u, v, and ware vectors such that Evaluate the given expression. u-v-2w, 4u+vi (u, v) -…

A:

Q: Find the centroid of the given region. (A) (5,15) (B) (3/22,45/61) (5/14,38/35) (8/23,76/111) y=2-x²…

A: Area under the curve y1=f1x and y2=f2x in the interval x∈a,b   A=∫abf2x-f1xdx x-coordinate of the…

Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cost) k…

A:

Q: 1. (a) Use differentiation to find a power series representation for 1 f(x) = (1+x)² ˚ What is the…

A:

Q: The value of China's exports of automobiles and parts (in billions of dollars) is where x = 0…

A: The function fx represents the exports.

Q: Problem 1 Suppose that y1, y2 are solutions to a homogeneous second-order linear differential…

A:

Q: (a) Consider (3,6) and (2,4) as elements of Z7xZ7. Compute (3,6) - (2,4). (b) Consider (3,6) and…

A:

Q: Evaluate the line integral y³ ds, for C: x = t³, y = t₁0 ≤ t ≤ 2.

A:

Q: Consider the following system. -5 x'-(10-12)x X'= Find the eigenvalues of the coefficient matrix…

A:

Q: pproximate cos(0.16) to five decimal-place accuracy using the MacLaurin series for cos(x). Os(0.16)…

A: Solution:-

Q: 9x+4y

A:

Q: Free Response Show all your work to support your final answer and 1. Let R be the region in the…

A:

Q: Compute the least-squares error associated with the least-squares solution x of Ax = b. 1 4 2 1,035…

A:

Q: G. Find a root of an equation f(x) = 10 - x² using Bisection method, ε = 0.01, and b = 5. a = -2

A:

Q: ГО Suppose A € M₁(R)and B. Find the eigenvalues of B =[2] of the eigenvalues of A. in terms

A: Suppose A∈MnR and B=0AA2A. We have to find the eigenvalues of B. We know that the eigenvalues of B…

Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cos t) k…

A: Finding unit tangent vector of above curve

Q: Use Stokes's Theorem to evaluate F(x, y, z) = z²i+yj + zk S: z = √4x² - y2 F. dr. In this case, C is…

A:

Q: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and…

A: To find  The amount accumulated FV in the given annuity account.

Q: MY NOTES ASK YOUR TEACHER Find the periodic payments PMT necessary to accumulate the given amount in…

A: