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)
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 N2–8Squeezing function g between functions f and h forces g to have the same
limit L at x = c as do f and g.