Questions from General Calculus

Q: Show that each function is continuous on its domain. State the

Show that each function is continuous on its domain. State the domain.

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. 2x3 + x2 + 2 = 0, (-2, -1)

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the equation in the given interval. e-x2 = x, (0, 1)

Q: According to Boyle’s Law, if the temperature of a confined gas

According to Boyle’s Law, if the temperature of a confined gas is held fixed, then the product of the pressure P and the volume V is a constant. Suppose that, for a certain gas, PV = 800, where P is m...

Q: The total cost of repaying a student loan at an interest rate

The total cost of repaying a student loan at an interest rate of r % per year is C = f (r). (a). What is the meaning of the derivative f'(r)? What are its units? (b). What does the statement f'(10) =...

Q: (a). Where does the normal line to the ellipse x2

(a). Where does the normal line to the ellipse x2 – xy + y2 3 at the point (-1, 1) intersect the ellipse a second time? (b). Illustrate part (a) by graphing the ellipse and the normal line.

Q: (a). Find the asymptotes of the graph of f (

(a). Find the asymptotes of the graph of f (x) = 4 – x/3 + x and use them to sketch the graph. (b). Use your graph from part (a) to sketch the graph of f'. (c). Use the definition of a derivative to f...

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: The cost of living continues to rise, but at a slower

The cost of living continues to rise, but at a slower rate. In terms of a function and its derivatives, what does this statement mean?

Q: The graph of the derivative f' of a function f is given

The graph of the derivative f' of a function f is given. (a). On what intervals is f increasing or decreasing? (b). At what values of x does f have a local maximum or minimum? (c). Where is f concav...