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))

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)

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

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)

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