Questions from Calculus

Q: Figure 8 shows a slope field of the differential equation y’ =

Figure 8 shows a slope field of the differential equation y’ = 2y (1 - y). With the help of this figure, determine the constant solutions, if any, of the differential equation. Verif...

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

Let f (t) be the solution of y’ = -(t + 1)y2, y(0) = 1. Use Euler’s method with n = 5 to estimate f (1). Then, solve the differential equation, find an explicit formula for f (t), and compute f (1)....

Q: Let f (t) be the solution of y’ = 10

Let f (t) be the solution of y’ = 10 - y, y(0) = 1. Use Euler’s method with n = 5 to estimate f (1). Then, solve the differential equation and find the exact value of f (1).

Q: Suppose that the Consumer Products Safety Commission issues new regulations that affect

Suppose that the Consumer Products Safety Commission issues new regulations that affect the toy-manufacturing industry. Every toy manufacturer will have to make certain changes in its manufacturing pr...

Q: The Los Angeles Zoo plans to transport a California sea lion to

The Los Angeles Zoo plans to transport a California sea lion to the San Diego Zoo. The animal will be wrapped in a wet blanket during the trip. At any time t, the blanket will lose water (due to evapo...

Q: The differential equation y’ = .5(1 - y)(

The differential equation y’ = .5(1 - y)(4 - y) has five types of solutions labeled A–E. For each of the following initial values, graph the solution of the differential equation and identify the typ...

Q: The differential equation y’ = .5(y - 1)(

The differential equation y’ = .5(y - 1)(4 - y) has five types of solutions labeled A–E. For each of the following initial values, graph the solution of the differential equation and identify the typ...

Q: The differential equation y’ = et - 2y, y(0

The differential equation y’ = et - 2y, y(0) = 1, has solution y = 1/3 (2e-2t + et ). In the following table, fill in the second row with the values obtained from the use of a numeri...

Q: The differential equation y’ = 2ty + et2, y(0

The differential equation y’ = 2ty + et2, y(0) = 5, has solution y = (t + 5)et2. In the following table, fill in the second row with the values obtained from the use of a numerical m...

Q: Suppose that f (t) is a solution of the differential

Suppose that f (t) is a solution of the differential equation y’ = ty - 5 and the graph of f (t) passes through the point (2, 4). What is the slope of the graph at this point?