In Exercises 1–6, use l’Hôpital’s Rule to evaluate the limit. Then evaluate the limit using a method studied in Chapter 2.


3. lim (x → ∞) (5x² - 3x) / (7x² + 1)

In Exercises 25–36, find the derivative of y with respect to the appropriate variable.

33. y = csch⁻¹(1/2)^θ

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

81. y = log₁₀(e^x)

Evaluate the integrals in Exercises 41–60.

43. ∫6cosh(x/2 - ln3)dx

In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.

70. y = ∛(x(x+1)(x-2)/(x²+1)(2x+3))

Evaluate the integrals in Exercises 87–96.

91. ∫₁^(√2) x·2^(x²) dx

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

75. y = x³ log₁₀ x