Questions from General Calculus

Q: The graph of f is shown. State, with reasons,

The graph of f is shown. State, with reasons, the numbers at which f is not differentiable.

Q: The figure shows the graphs of f, f’, and f’’

The figure shows the graphs of f, f’, and f’’. Identify each curve, and explain your choices.

Q: Sketch the graph of a function f that satisfies all of the

Sketch the graph of a function f that satisfies all of the following conditions: The domain of f is all real numbers except 0, / for all x in the domain of f/

Q: If a ball is thrown into the air with a velocity of

If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet t seconds later is given by y = 40t - 16t2. a. Find the average velocity for the time period beginning when t = 2 and l...

Q: a. Evaluate h(x) = (tan x -

a. Evaluate h(x) = (tan x - x)/x3 for x = 1, 0.5, 0.1, 0.05, 0.01, and 0.005. b. Guess the value of c. Evaluate h(x) for successively smaller values of x until you finally reach a value of 0 for h(x...

Q: Let P(t) be the percentage of Americans under the

Let P(t) be the percentage of Americans under the age of 18 at time t. The table gives values of this function in census years from 1950 to 2010. a. What is the meaning of P’(t)? W...

Q: Let B(t) be the number of US $20

Let B(t) be the number of US $20 bills in circulation at time t. The table gives values of this function from 1990 to 2010, as of December 31, in billions. Interpret and estimate the value of Bâ...

Q: The total fertility rate at time t, denoted by F(

The total fertility rate at time t, denoted by F(t), is an estimate of the average number of children born to each woman (assuming that current birth rates remain constant). The graph of the total fer...

Q: Suppose that |f(x)|≤ g(x) for

Suppose that |f(x)|≤ g(x) for all x, where limx→a g(x) = 0. Find limx→a f(x).

Q: Let / a. For what values of

Let a. For what values of a does limx→a f(x) exist? b. At what numbers is f discontinuous?