Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)
15. lim(x→∞)arctan(x)

Theory and Applications

L’Hôpital’s Rule does not help with the limits in Exercises 69–76. 

Try it—you just keep on cycling. Find the limits some other way.

75. lim (x → ∞) e^(x²) / (x e^x)

82. For what values of a and b is

lim(x→0)(tan(2x/x³) + a/x² + sin(bx)/x) = 0?

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.)

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)