Use l’Hôpital’s Rule to find the limits in Exercises 85–108.
102. lim(x→0) (x sin(x²))/(tan³x)

Evaluate the integrals in Exercises 31–78.

45. ∫(ln x)^(-3)/x dx

Use l’Hôpital’s Rule to find the limits in Exercises 85–108.

97. lim(x→0) (10^x - 1)/x

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

1. y = 10e^(-x/5)

133. What is the age of a sample of charcoal in which 90% of the carbon-14 originally present has decayed?

In Exercises 79–84, solve for y.

79. 3^y = 2^(y+1)

In Exercises 79–84, solve for y.

83. ln(y-1) = x + ln(y)