Barrons AP Calculus

(Marvins-Underground-K-12) #1

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).


Sandwich    (Squeeze)   Theorem

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