4. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?
c. x²e^(-x)

86. This exercise explores the difference between

lim(x→∞)(1 + 1/x²)^x

and

lim(x→∞)(1 + 1/x)^x = e

c. Confirm your estimate of lim(x→∞)f(x) by calculating it with l’Hôpital’s Rule.

Suppose that the function f and its derivative with respect to x have the following values at x=0, 1, 2, 3, and 4.

Assuming the inverse function f^(-1) is differentiable, find the slope of f^(-1)(x) at

c. x=3

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

3. c. sin^(-1)(-√3/2)

82. Use the definitions of the hyperbolic functions to find each of the following limits.

c. lim(x→∞) sinh x

In Exercises 1–4, solve for t.

1. c. e^((ln 0.2)t) = 0.4

23. Human evolution continues The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is continuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years.

c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?