Questions from General Calculus

Q: Define the derivative f'(a). Discuss two ways of interpreting

Define the derivative f'(a). Discuss two ways of interpreting this number.

Q: Define the second derivative of f. If f (t)

Define the second derivative of f. If f (t) is the position function of a particle, how can you interpret the second derivative?

Q: (a). What does it mean for f to be differentiable

(a). What does it mean for f to be differentiable at a? (b). What is the relation between the differentiability and continuity of a function? (c). Sketch the graph of a function that is continuous but...

Q: Describe several ways in which a function can fail to be differentiable

Describe several ways in which a function can fail to be differentiable. Illustrate with sketches.

Q: (a). What does the sign of f'(x)

(a). What does the sign of f'(x) tell us about f? (b). What does the sign of f"(x) tell us about f?

Q: (a). Define an antiderivative of f. (b

(a). Define an antiderivative of f. (b). What is the antiderivative of a velocity function? What is the antiderivative of an acceleration function?

Q: Describe several ways in which a limit can fail to exist.

Describe several ways in which a limit can fail to exist. Illustrate with sketches.

Q: (a). What does it mean to say that the line

(a). What does it mean to say that the line x = a is a vertical asymptote of the curve y = f (x)? Draw curves to illustrate the various possibilities. (b). What does it mean to say that the line y = L...

Q: An approach path for an aircraft landing is shown in the figure

An approach path for an aircraft landing is shown in the figure and satisfies the following conditions: (i). The cruising altitude is h when descent starts at a horizontal distance from touchdown at...

Q: The solution in Problem 1 might look smooth, but it might

The solution in Problem 1 might look smooth, but it might not feel smooth because the piecewise defined function [consisting of L1 (x) for x 100] doesn’t have a continuous second de...