Barrons AP Calculus - David Bock

FIGURE N2–7

C. THEOREMS ON LIMITS

If lim f (x) and lim g(x) are finite numbers, then:

(1) lim kf (x) = k lim f (x).

(2) lim[f (x) + g(x)] = lim f (x) + lim g(x).

(3) lim f (x)g(x) = (lim f (x))(lim g(x)).

(4) (if lim g(x) ≠ 0).

(5)

(6) THE SQUEEZE OR SANDWICH THEOREM. If f (x) ≤ g(x) ≤ h(x) and if

Figure N2–8 illustrates this theorem.

FIGURE N2–8

Squeezing function g between functions f and h forces g to have the same limit L at x = c as do f

and g.

EXAMPLE 9