Questions from Calculus

Q: A cell phone service charges $10 for the first gigabyte (

A cell phone service charges $10 for the first gigabyte (GB) of data used per month and $7.50 for each additional gigabyte or fraction thereof. The cost of the data plan is given by C(t) = 10 − 7.5 [[...

Q: The number of units in inventory in a small company is given

The number of units in inventory in a small company is given by where t is the time in months. Sketch the graph of this function and discuss its continuity. How often must this company replenish its i...

Q: At 8:00 a.m. on Saturday, a

At 8:00 a.m. on Saturday, a man begins running up the side of a mountain to his weekend campsite (see figure). On Sunday morning at 8:00 a.m., he runs back down the mountain. It takes him 20 minutes t...

Q: Use the Intermediate Value Theorem to show that for all spheres with

Use the Intermediate Value Theorem to show that for all spheres with radii in the interval [5, 8], there is one with a volume of 1500 cubic centimeters.

Q: Prove that if f is continuous and has no zeros on [

Prove that if f is continuous and has no zeros on [a, b], then either f(x) > 0 for all x in [a, b] or f(x) < 0 for all x in [a, b].

Q: Show that the Dirichlet function / is not continuous at

Show that the Dirichlet function is not continuous at any real number.

Q: Sketch the graph of f′. Explain how you found your answer

Sketch the graph of f′. Explain how you found your answer.

Q: Show that the function / is continuous only at x

Show that the function is continuous only at x = 0. (Assume that k is any nonzero real number.)

Q: The signum function is defined by / Sketch a graph

The signum function is defined by Sketch a graph of sgn(x) and find the following (if possible).

Q: The table lists the frequency F (in Hertz) of a

The table lists the frequency F (in Hertz) of a musical note at various times t (in seconds). a. Plot the data and connect the points with a curve. b. Does there appear to be a limiting frequency of t...