Questions from Calculus

Q: One or more initial conditions are given for each differential equation in

One or more initial conditions are given for each differential equation in the following exercises. Use the qualitative theory of autonomous differential equations to sketch the graphs of the correspo...

Q: Suppose that, once a sunflower plant has started growing, the

Suppose that, once a sunflower plant has started growing, the rate of growth at any time is proportional to the product of its height and the difference between its height at maturity and its current...

Q: A parachutist has a terminal velocity of -176 feet per second

A parachutist has a terminal velocity of -176 feet per second. That is, no matter how long a person falls, his or her speed will not exceed 176 feet per second, but it will get arbitrarily close to th...

Q: Draw the graph of g(x) = (x -

Draw the graph of g(x) = (x - 2)2 (x - 6)2, and use the graph to sketch the solutions of the differential equation y’ = (y - 2)2 (y - 6)2 with initial conditions y(0) = 1, y(0) = 3, y(0) = 5, and y(0...

Q: Draw the graph of g(x) = ex - 100x2

Draw the graph of g(x) = ex - 100x2 - 1, and use the graph to sketch the solution of the differential equation y’ = ey - 100y2 - 1 with initial condition y(0) = 4 on a ty-coordinate system.

Q: Sketch the graph of a function with the stated properties.

Sketch the graph of a function with the stated properties. Domain: 0 ≤ t ≤ 3; (0, 1) is on the graph; the slope is always positive, and the slope becomes less positive (as t increases).

Q: Sketch the graph of a function with the stated properties.

Sketch the graph of a function with the stated properties. Domain: 0 ≤ t ≤ 4; (0, 2) is on the graph; the slope is always positive, and the slope becomes more positive (as t increases).

Q: On the slope field in Fig. 5(a) or

On the slope field in Fig. 5(a) or a copy of it, draw the solution of the initial-value problem y’ = .0002y (5000 - y), y(0) = 500. Figure 5:

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...