Questions from General Calculus

Q: Use the partial fraction command on your CAS to find a convenient

Use the partial fraction command on your CAS to find a convenient expression for the partial sum, and then use this expression to find the sum of the series. Check your answer by using the CAS to sum...

Q: Suppose you throw a ball into the air. Do you think

Suppose you throw a ball into the air. Do you think it takes longer to reach its maximum height or to fall back to earth from its maximum height? We will solve the problem in this project but, before...

Q: In this project we explore three of the many applications of calculus

In this project we explore three of the many applications of calculus to baseball. The physical interactions of the game, especially the collision of ball and bat, are quite complex and their models a...

Q: If water (or other liquid) drains from a tank,

If water (or other liquid) drains from a tank, we expect that the flow will be greatest at first (when the water depth is greatest) and will gradually decrease as the water level decreases. But we nee...

Q: 1. All solutions of the differential equation y' = -1

1. All solutions of the differential equation y' = -1 – y4 are decreasing functions. 2. The function f (x) = (ln x)/x is a solution of the differential equation x2y' + xy = 1. 3. The...

Q: (a). Sketch a direction field for the differential equation y'

(a). Sketch a direction field for the differential equation y' = x/y. Then use it to sketch the four solutions that satisfy the initial conditions y (0) = 1, y (0) = -1, y (2) = 1, and y (-2) = 1. (b)...

Q: (a). A direction field for the differential equation y' =

(a). A direction field for the differential equation y' = x2 – y2 is shown. Sketch the solution of the initial-value problem Use your graph to estimate the value of y (0.3). (b)....

Q: (a). What is a differential equation? (b

(a). What is a differential equation? (b). What is the order of a differential equation? (c). What is an initial condition?

Q: Solve the differential equation. 2 yey2y' = 2x + 3

Solve the differential equation. 2 yey2y' = 2x + 3√x

Q: A subtangent is a portion of the x-axis that lies

A subtangent is a portion of the x-axis that lies directly beneath the segment of a tangent line from the point of contact to the x-axis. Find the curves that pass through the point (c, 1) and whose s...