12.1 Continued

Properties of Limits

There are 4 properties:

Lim b = b
x→ c

Lim x = c
x→ c

Lim xⁿ = cⁿ

x→ c






Ex:
(1st property)
Lim 5 = 5
x→2


(2nd property)
Lim x = 2
x→3

(3rd property)
Lim x^{2 = 9}
x→3

(4th property)

^{Lim (cubed root x) = 2}
x→8

Operations with Limits

Lim f(x) = L
x→c

and

Lim g(x) = K
x→c

Scalar Multiple:
Lim [bf(x)]= bL
x→c

Sum or difference:
Lim [f(x) ± g(x)] = L ± K

x→c

Product:
Lim [f(x)g(x0] = LK

x→c

Quotient:
Lim [f(x)/g(x)] = L/K
x→c
****with this one K can not be 0

Power:
Lim [F(x)]ⁿ = Lⁿ
x→c



Continuity

Function is continuous if:
Lim f(x) = f(a)
x→a

For extra help with continuity
http://www.youtube.com/watch?v=hlorAjS0xWE&feature=related