77. Which one is correct, and which one is wrong? Give reasons for your answers.
a. lim (x → 3) (x - 3) / (x² - 3) = lim (x → 3) 1 / (2x) = 1/6

89. Use limits to find horizontal asymptotes for each function.

a. y = x tan(1/x)

9. True, or false? As x→∞,

a. x = o(x)

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

5. a. arccos(1/2)

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?

a. 10x^4 + 30x + 1

[Technology Exercise] In Exercises 139–141, find the domain and range of each composite function. Then graph the compositions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see.

141. a. y=arccos(cos x)

21. a. Show that ln(x) grows slower as x→∞ than x^(1/n) for any positive integer n, even x^(1/1,000,000).