Questions from General Calculus

Q: In contrast to the situation of Exercise 40, experiments show that

In contrast to the situation of Exercise 40, experiments show that the reaction H2 + Br2 → 2HBr satisfies the rate law and so, for this reaction the differential equation becomes...

Q: A sphere with radius 1 m has temperature 150C. It lies

A sphere with radius 1 m has temperature 150C. It lies inside a concentric sphere with radius 2 m and temperature 250C. The temperature T (r) at a distance r from the common center of the spheres sati...

Q: A direction field for the differential equation y' = x cos πy

A direction field for the differential equation y' = x cos πy is shown. (a). Sketch the graphs of the solutions that satisfy the given initial conditions. (b). Find all the equilibrium...

Q: A function satisfies the differential equation dy/dt = y4 –

A function satisfies the differential equation dy/dt = y4 – 6y3 + 5y2 (a). What are the constant solutions of the equation? (b). For what values of y is increasing? (c). For what values of y is decrea...

Q: Sketch the direction field of the differential equation. Then use it

Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes through the given point.

Q: Sketch the direction field of the differential equation. Then use it

Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes through the given point.

Q: Match the differential equations with the solution graphs labeled I–IV

Match the differential equations with the solution graphs labeled I–IV. Give reasons for your choices.

Q: Sketch the direction field of the differential equation. Then use it

Sketch the direction field of the differential equation. Then use it to sketch a solution curve that passes through the given point.

Q: Show that y = 2/3 ex + e-2x

Show that y = 2/3 ex + e-2x is a solution of the differential equation y' = + 2y = 2ex.

Q: Suppose ∑an and ∑bn are series with positive terms and

Suppose ∑an and ∑bn are series with positive terms and ∑bn is known to be convergent. (a). If an > bn for all n, what can you say about ∑an? Why? (b). If an < bn for all n, what can you say about ∑an?...