Questions from General Calculus

Q: If y = 2(1 - e-x), compute

If y = 2(1 - e-x), compute y and show that y’ = 2 - y.

Q: If y = 5(1 - e-2x), compute

If y = 5(1 - e-2x), compute y and show that y’ = 10 - 2y.

Q: If f (x) = 3(1 - e-

If f (x) = 3(1 - e-10x), show that y = f (x) satisfies the differential equation y’ = 10(3 - y), f (0) = 0.

Q: The following function may be viewed as a composite function h (

The following function may be viewed as a composite function h (x) = f ( g (x)). Find f (x) and g (x). h(x) = (x3 + 8x - 2)5

Q: A student learns a certain amount of material for some class.

A student learns a certain amount of material for some class. Let f (t) denote the percentage of the material that the student can recall t weeks later. The psychologist Hermann Ebbinghaus found that...

Q: When a grand jury indicted the mayor of a certain town for

When a grand jury indicted the mayor of a certain town for accepting bribes, the newspaper, online news outlets, radio, and television immediately began to publicize the news. Within an hour, one-quar...

Q: Examine formula (8) for the amount A(t)

Examine formula (8) for the amount A(t) of excess glucose in the bloodstream of a patient at time t. Describe what would happen if the rate r of infusion of glucose were doubled.

Q: A news item is spread by word of mouth to a potential

A news item is spread by word of mouth to a potential audience of 10,000 people. After t days, f (t) = 10,000 / (1 + 50e-0.4t) people will have heard the news. The graph of this function is shown in...

Q: Find ln(√e).

Find ln(√e).

Q: The width of a rectangle is increasing at a rate of 3

The width of a rectangle is increasing at a rate of 3 inches per second and its length is increasing at the rate of 4 inches per second. At what rate is the area of the rectangle increasing when its w...