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

f. lim(x→∞) coth x

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

f. (e^x)/2

2. Express the following logarithms in terms of ln 5 and ln 7.

f. (ln35 + ln(1/7))/(ln25)

1. Express the following logarithms in terms of ln 2 and ln 3.

f. ln √(13.5)

3. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

g. x^3 e^(-x)

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?

g. e^(cos(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?

g. ln(ln x)

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

g. 1/x

9. True, or false? As x→∞,

g. ln(x) = o(ln(2x))

4. Which of the following functions grow faster than x² as x→∞? Which grow at the same rate as x²? Which grow slower?

g. (1.1)^x

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

h. lim(x→0^-) coth x

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

i. lim(x→-∞) csch x

Use the table of integrals at the back of the text to evaluate the integrals in Exercises 1–26.

∫ sin(2x) cos(3x) dx

Evaluate the integrals in Exercises 31–56. Some integrals do not require integration by parts.

∫ sin(2x) cos(4x) dx

Evaluate the integrals in Exercises 69–134. The integrals are listed in random order so you need to decide which integration technique to use.

∫ (tan²x + sec²x) dx