[You may assume that tan x ---. L as x ---.

a, x E (-7f/2,7f/2), if and only if arctan x ---. a as x ---. L,]

(e)

sinx lim -2-'

x-+oo

[!]. This exercise is used in many places. Recall that a polynomial of degree n is a function of the form P(x) = anxn + an_lXn- 1 + ... + alX + ao where aj E R for j = 0,1, ... , n and an =f. O.