Evaluate the integrals in Exercises 41–60.
49. ∫(sech(√t)tanh(√t)dt)/√t

Indeterminate Powers and Products

Find the limits in Exercises 53–68.

53. lim (x → 1⁺) x^(1/(1 - x))

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

44. lim (x → 0⁺) (csc x - cot x + cos x)

Evaluate the integrals in Exercises 53–76.

67. ∫dx/(2+(x-1)²)

Evaluate the integrals in Exercises 77–90.

90. ∫dx/((x-2)√(x²-4x+3))

80. Volume The region enclosed by the curve y=sech(x), the x-axis, and the lines x=±ln√3 is revolved about the x-axis to generate a solid. Find the volume of the solid.

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

15. y = 2√t tanh(√t)