Questions from General Calculus

Q: Let p and q be real numbers with p < q.

Let p and q be real numbers with p

Q: Use Euler’s method with step size 0.2 to estimate y

Use Euler’s method with step size 0.2 to estimate y (1), where y (x) is the solution of the initial-value problem y' = xy – x2, y (0) = 1.

Q: Use Euler’s method with step size 0.1 to estimate y

Use Euler’s method with step size 0.1 to estimate y (0.5), where y (x) is the solution of the initial-value problem y' = y + xy, y (0) = 1.

Q: The figure shows a circuit containing an electromotive force, a capacitor

The figure shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ω). The voltage drop acros...

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

(a). For what values of does the function y = cos kt satisfy the differential equation 4y" = -25? (b). For those values of k, verify that every member of the family of functions y = A sin kt + B cos k...

Q: Match the differential equation with its direction field (labeled I–

Match the differential equation with its direction field (labeled I–IV). Give reasons for your answer.

Q: Which of the following functions are solutions of the differential equation y

Which of the following functions are solutions of the differential equation y" + y = sin x?

Q: (a). Show that every member of the family of functions

(a). Show that every member of the family of functions y = (ln x + C)/x is a solution of the differential equation x2y' + xy = 1. (b). Illustrate part (a) by graphing several members of the family of...

Q: A population is modeled by the differential equation dP/dt =

A population is modeled by the differential equation dP/dt = 1.2P (1 – P/4200) (a). For what values of P is the population increasing? (b). For what values of P is the population decreasing? (c). What...

Q: Match the differential equation with its direction field (labeled I–

Match the differential equation with its direction field (labeled I–IV). Give reasons for your answer. y' = x (2 - y)