"Hand-in question" (only 4(a)): Use singular perturbation methods to obtain zeroth orderapproximations, valid for t e [0, 1], to the following boundary-value problems in which 0 < e <1.(a)eä + i = 2(1 – t), x(0) = 1, x(1) = 1

To find- Use singular perturbation methods to obtain zeroth order approximations, valid for t ∈ 0,…

Answered: "Hand-in question" (only 4(a)): Use…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P, has doubled in 5 years. Suppose it is known that the population is 12,000 after 3 years. What was the initial population Po? (Round your answer to one decimal place.) Po What will be the population in 10 years? (Round your answer to the nearest person.) persons How fast is the population growing at t= 10? (Round your answer to the nearest person.) persons/year Need Help? Read It Watch It
3) Solve the following boundary-value problems. b) y"(x) + 2y(x) = 0; y(0) = 0; y'(z) = 0.
(4) Solve the following Boundary Value Problems (and calculate D to verify the correct number of solutions): (a) x(0) + r'(0) = 8, x" + 4x = 3 sint (T) + x'(T) = 6 (b) r(0) + r'(0) = 8, (T) + x'(T) = 8 (c) x(0) + x'(0) = 8, x(x) + 2x' (n) = 11 (5) Solve the following Boundary Value Problems (and calculate D to verify the correct number of solutions): x" - x = 6et (a) x(0) + x'(0) = 5, x(1) + x'(1) = 10e (b) x(0) + x'(0) = 5, x(1) + x'(1) = 11e (c) x(0) + r'(0) = 5, x(1) - x'(1) = e
Q2: y" +9y et Where y(0)=0 and y'(0)=0 =
The dynamics of a fish population is described by the Richard's growth law dN N rN (1) dt K where N = N(t) is the population size depending on the continuous time variable t, and r and K are positive constants.
15. Find the value(s) of such that the solution of the initial-value problem y" - 4y= sin x; y(0) = y, y'(0) = 0 is bounded on [0, ∞).
we have a polynomial f(x) of degree d is equal to 1 1 Pa(x) = f(0) + f'(0)x + "(0)x² + ... +f (0)x“ . d!- If f is a general function that has dth order derivatives at 0, then the polynomial P(x) approximates f(x) for small x. As d increases, these approximations get better, assuming f is a reasonable function. The polynomial Pa is called the degree d Taylor approximation of f at 0. (A) Find the degree 4 Taylor approximations at 0 of cos x. (B) Approximate cos(0.1) using your answer to part (A). For comparison, wolfram alpha tells me cos(0.1) = 0.995004165278....
How large should n be to guarantee that the Trapezoidal Rule approximation to x - 12x- 48x² + 2x + 5) dæ is accurate to within 0.1. n = How large should n be to guarantee that the Simpsons Rule approximation to 2 1(-a - 12a - 48z? + 2x + 5) dx is accurate to within 0.1. n = Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n Question Help: Video 1 D Video 2 Submit Question P Type here to search hp

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"Hand-in question" (only 4(a)): Use singular perturbation methods to obtain zeroth order approximations, valid for t € [0, 1], to the following boundary-value problems in which 0 < ɛ < 1. (a) ε*+ * = 2(1-t), x(0)=1, x(1) = 1

"Hand-in question" (only 4(a)): Use singular perturbation methods to obtain zeroth order approximations, valid for t € [0, 1], to the following boundary-value problems in which 0 < ɛ < 1. (a) ε+ = 2(1-t), x(0)=1, x(1) = 1