Questions from General Calculus

Q: The cost of producing x ounces of gold from a new gold

The cost of producing x ounces of gold from a new gold mine C = f (x) is dollars. (a). What is the meaning of the derivative f'(x)? What are its units? (b). What does the statement f' (800) = 17 mean?...

Q: The number of bacteria after t hours in a controlled laboratory experiment

The number of bacteria after t hours in a controlled laboratory experiment is n = f (t). (a). What is the meaning of the derivative f' (5)? What are its units? (b). Suppose there is an unlimited amoun...

Q: A function is a ratio of quadratic functions and has a vertical

A function is a ratio of quadratic functions and has a vertical asymptote x = 4 and just one x-intercept, x = 1. It is known that f has a removable discontinuity at x = -1 and limx→1 f (x) = 2. Evalua...

Q: Use the given graph of f to state the value of each

Use the given graph of f to state the value of each quantity, if it exists. If it does not exist, explain why.

Q: The quantity (in pounds) of a gourmet ground coffee that

The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q = f (p). (a). What is the meaning of the derivative f' (8)? What are its uni...

Q: Let P and Q be polynomials. Find limx→∞ P (

Let P and Q be polynomials. Find limx→∞ P (x)/Q (x) if the degree of P is (a) less than the degree of Q and (b) greater than the degree of Q.

Q: The graph shows the influence of the temperature T on the maximum

The graph shows the influence of the temperature T on the maximum sustainable swimming speed of Coho salmon. (a). What is the meaning of the derivative S'(T)? What are its units? (b). Estimate the v...

Q: Show that the function is continuous on (-∞, ∞). /

Show that the function is continuous on (-∞, ∞).

Q: (a). Show that the absolute value function F (x

(a). Show that the absolute value function F (x) = |x| is continuous everywhere. (b). Prove that if f is a continuous function on an interval, then so is |f|. (c). Is the converse of the statement in...

Q: (a). A tank contains 5000 L of pure water.

(a). A tank contains 5000 L of pure water. Brine that contains 30 g of salt per liter of water is pumped into the tank at a rate of 25 L/min. Show that the concentration of salt after t minutes (in gr...