Questions from General Calculus

Q: Homeostasis refers to a state in which the nutrient content of a

Homeostasis refers to a state in which the nutrient content of a consumer is independent of the nutrient content of its food. In the absence of homeostasis, a model proposed by Sterner and Elser is gi...

Q: Let A (t) be the area of a tissue culture

Let A (t) be the area of a tissue culture at time t and let M be the final area of the tissue when growth is complete. Most cell divisions occur on the periphery of the tissue and the number of cells...

Q: According to Newton’s Law of Universal Gravitation, the gravitational force on

According to Newton’s Law of Universal Gravitation, the gravitational force on an object of mass m that has been projected vertically upward from the earth’s surfac...

Q: Verify that y = -t cos t – t is a

Verify that y = -t cos t – t is a solution of the initial-value problem

Q: Use a computer algebra system to draw a direction field for the

Use a computer algebra system to draw a direction field for the differential equation y' = y3 – 4y. Get a printout and sketch on its solutions that satisfy the initial condition y (0) = c for various...

Q: (a). For what values of does the function y =

(a). For what values of does the function y = erx satisfy the differential equation 2y" + y' – y = 0? (b). If r1 and r2 are the values of r that you found in part (a), show that every member of the fa...

Q: (a). Use Euler’s method with each of the following step

(a). Use Euler’s method with each of the following step sizes to estimate the value of y (0.4), where is the solution of the initial-value problem y' = y, y (0) = 1. (b). We know t...

Q: A direction field for the differential equation y' = tan (1

A direction field for the differential equation y' = tan (1/2 πy) is shown. (a). Sketch the graphs of the solutions that satisfy the given initial conditions. (b). Find all the equilibr...

Q: A direction field for a differential equation is shown. Draw,

A direction field for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step sizes h = 1 and h = 0....

Q: Use Euler’s method with step size 0.5 to compute the

Use Euler’s method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem y' = y – 2x, y (1) = 0.