In Exercises 1–24, find the derivative of y with respect to the appropriate variable.
19. y = t arctan(t) - 1/2 ln(t)

In Exercises 129–132 solve the initial value problem.

131. x dy - (y + √y)dx = 0, y(1) = 1

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

95. lim(x→∞) (√(x² + x + 1) - √(x² - x))

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

88. lim(x→0) (tan x)/(x + sin(x))

Evaluate the integrals in Exercises 31–78.

77. ∫dt/((t+1)√(t²+2t-8))

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

23. y = arccsc(secθ), 0<θ<π/2

In Exercises 115 and 116, find the absolute maximum and minimum values of each function on the given interval.

116. y = 10x (2 - ln(x)), (0, e²]"133. Find the absolute maximum value of

f(x) = x^2 * ln(1/x)

and say where it is assumed