Indeterminate Powers and Products
Find the limits in Exercises 53–68.
63. lim (x → ∞) ((x + 2)/(x - 1))^x

Evaluate the integrals in Exercises 33–54.

53. ∫ (e^r / (1 + e^r)) dr

Evaluate the integrals in Exercises 41–60.

41. ∫sinh(2x)dx

In Exercises 27–32, find dy/dx.

3+siny = y-x^3

Evaluate the integrals in Exercises 41–60.

57. ∫(from 1 to 2)cosh(ln t)/t dt

37. Plutonium-239 The half-life of the plutonium isotope is 24,360 years. If 10 g of plutonium is released into the atmosphere by a nuclear accident, how many years will it take for 80% of the isotope to decay?

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = e^(cost+lnt)