Questions from Calculus

Q: A single dose of iodine is injected intravenously into a patient.

A single dose of iodine is injected intravenously into a patient. The iodine mixes thoroughly in the blood before any is lost as a result of metabolic processes (ignore the time required for this mixi...

Q: Show that the mathematical model in Check Your Understanding 2 predicts that

Show that the mathematical model in Check Your Understanding 2 predicts that the amount of litter in the forest will eventually stabilize. What is the “equilibrium level” of litter in that problem? [N...

Q: In the study of the effect of natural selection on a population

In the study of the effect of natural selection on a population, we encounter the differential equation dq/dt = -.0001q2 (1 - q), where q is the frequency of a gene a and the selection pressure is a...

Q: You are given a logistic equation with one or more initial conditions

You are given a logistic equation with one or more initial conditions. (a) Determine the carrying capacity and intrinsic rate. (b) Sketch the graph of dN/dt versus N in an Nz-plane. (c) In the tN-p...

Q: You are given a logistic equation with one or more initial conditions

You are given a logistic equation with one or more initial conditions. (a) Determine the carrying capacity and intrinsic rate. (b) Sketch the graph of dN/dt versus N in an Nz-plane. (c) In the tN-p...

Q: Suppose that f (t) satisfies the initial-value problem

Suppose that f (t) satisfies the initial-value problem y = y2 + ty - 7, y(0) = 2. Is the graph of f (t) increasing or decreasing at t = 0?

Q: Use Euler’s method with n = 2 on the interval 0 ≤

Use Euler’s method with n = 2 on the interval 0 ≤ t ≤ 1 to approximate the solution f (t) to y = t2y, y(0) = -2. In particular, estimate f (1).

Q: Use Euler’s method with n = 2 on the interval 2 ≤

Use Euler’s method with n = 2 on the interval 2 ≤ t ≤ 3 to approximate the solution f (t) to y’ = t - 2y, y(2) = 3. Estimate f (3).

Q: Use Euler’s method with n = 4 to approximate the solution f

Use Euler’s method with n = 4 to approximate the solution f (t) to y’ = 2t - y + 1, y(0) = 5 for 0 ≤ t ≤ 2. Estimate f (2).

Q: Let f (t) be the solution of y’ = y

Let f (t) be the solution of y’ = y(2t - 1), y(0) = 8. Use Euler’s method with n = 4 to estimate f (1).