Questions from General Calculus

Q: Evaluate the following improper integrals whenever they are convergent. ∫

Evaluate the following improper integrals whenever they are convergent. ∫1 ∞ (x + 2)/(x2 + 4x – 2) dx

Q: Determine the integrals by making appropriate substitutions. ∫ (3

Determine the integrals by making appropriate substitutions. ∫ (3 - x) (x2 - 6x)4 dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫

Evaluate the following improper integrals whenever they are convergent. ∫1 ∞ x2 e-x3 dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫-

Evaluate the following improper integrals whenever they are convergent. ∫-1 ∞ (x + 3)-5/4 dx

Q: Evaluate the following improper integrals whenever they are convergent. ∫-∞

Evaluate the following improper integrals whenever they are convergent. ∫-∞ 0 8/(5 - 2x)3 dx

Q: It can be shown that lim b→∞ b e-b

It can be shown that lim b→∞ b e-b = 0. Use this fact to compute ∫1 ∞ x e-x dx.

Q: Let k be a positive number. It can be shown that

Let k be a positive number. It can be shown that lim b→∞ b e-kb = 0. Use this fact to compute ∫0 ∞ x e-kx dx.

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

Find the present value of a continuous stream of income over the next 4 years, where the rate of income is 50e-0.08t thousand dollars per year at time t, and the interest rate is 12%.

Q: Suppose that t miles from the center of a certain city the

Suppose that t miles from the center of a certain city the property tax revenue is approximately R(t) thousand dollars per square mile, where R(t) = 50 e-t/20. Use this model to predict the total prop...

Q: Suppose that a machine requires daily maintenance, and let M(

Suppose that a machine requires daily maintenance, and let M(t) be the annual rate of maintenance expense at time t. Suppose that the interval 0 ≤ t ≤ 2 is divided into n subintervals, with endpoints...