Questions from General Calculus

Q: Divide the given interval into n subintervals and list the value of

Divide the given interval into n subintervals and list the value of Δx and the endpoints a0, a1, …. , an of the subintervals. -1 ≤ x ≤ 2; n = 5

Q: Find the present value of a continuous stream of income over 3

Find the present value of a continuous stream of income over 3 years if the rate of income is 80 e-0.08t thousand dollars per year at time t and the interest rate is 11%.

Q: A continuous stream of income is produced at the rate of 20

A continuous stream of income is produced at the rate of 20 e1-0.09 t thousand dollars per year at time t, and invested money earns 6% interest. (a) Write a definite integral that gives the present va...

Q: A growth company is one whose net earnings tend to increase each

A growth company is one whose net earnings tend to increase each year. Suppose that the net earnings of a company at time t are being generated at the rate of 30 + 5t million dollars per year. (a) Wri...

Q: Find the present value of a stream of earnings generated over the

Find the present value of a stream of earnings generated over the next 2 years at the rate of 50 + 7t thousand dollars per year at time t assuming a 10% interest rate.

Q: In 2012, the population density of a city t miles from

In 2012, the population density of a city t miles from the city center was 120 e-0.65t thousand people per square mile. (a) Write a definite integral whose value equals the number of people (in thousa...

Q: Use the population density from Exercise 9 to calculate the number of

Use the population density from Exercise 9 to calculate the number of people who lived between 3 and 5 miles from the city center. Exercise 9: In 2012, the population density of a city t miles from t...

Q: The population density of Philadelphia in 1940 was given by the function

The population density of Philadelphia in 1940 was given by the function 60 e-0.4t. Calculate the number of people who lived within 5 miles of the city center. Sketch the graphs of the population dens...

Q: A volcano erupts and spreads lava in all directions. The density

A volcano erupts and spreads lava in all directions. The density of the deposits at a distance t kilometers from the center is D (t) thousand tons per square kilometer, where D (t) = 11(t2 + 10)-2. Fi...

Q: Determine the following indefinite integrals: ∫ x2 ln x2 dx

Determine the following indefinite integrals: ∫ x2 ln x2 dx