1. Limits and Continuity

84. Find lim(x→∞) (√(x² + 1) - √x).

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

13. lim(x → 1⁻)arcsin(x)

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

15. lim(x→∞)arctan(x)

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

17. lim(x→∞)arcsec(x)

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

19. lim(x→∞)arccsc(x)

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

a. lim(x→∞) tanh x

9. True, or false? As x→∞,

a. x = o(x)

9. True, or false? As x→∞,

c. x = O(x+5)

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

c. lim(x→∞) sinh x

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

f. lim(x→∞) coth x

9. True, or false? As x→∞,

e. e^x = o(e^(2x))

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

h. lim(x→0^-) coth x

9. True, or false? As x→∞,

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

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

i. lim(x→-∞) csch x

10. True, or false? As x→∞,

a. 1/(x+3) = O(1/x)