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

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

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

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

19. y = t arctan(t) - 1/2 ln(t)

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

88. lim(x→0) (tan x)/(x + sin(x))

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

104. lim(x→4) (sin²(πx))/(e^(x-4) + 3 - x)

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

15. y = sin⁻¹√(1-u²), 0<u<1