88. Given that x>0, find the maximum value, if any, of
c. x^(1/x^n) (n a positive integer)

What can you conclude about the inverses of functions whose graphs are lines perpendicular to the line y=x?

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

1. c. tan^(-1)(1/√3)

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

c. lim(x→∞) sinh x

6. Which of the following functions grow faster than ln(x) as x→∞? Which grow at the same rate as ln(x)? Which grow slower?

c. 1/√x

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)?

2. Which of the following functions grow faster than e^x as x→∞? Which grow at the same rate as e^x? Which grow slower?

c. √(1+x^4)