Microsoft Word - Understanding Limits

UNDERSTANDING LIMITS

Example:

(a) (d) (g)

Given the graph of y = f ( x) below, evaluate the following limits.

lim f ( x ) =0

(b)

lim f ( x ) =1

(e)

x →1

x →−4 −

lim f ( x ) =-∞=DNE (h)

x →−2 −

lim f ( x ) =-∞=DNE (c) x →3

lim f ( x ) =-1

x →−4+

(f)

lim f ( x ) =∞=DNE (i)

x →−2+

lim f ( x) =2 x →∞

lim f ( x ) =DNE

x →−4

lim f ( x ) =DNE

x →−2

Algebraic Limits: (a)

x−4 lim 2 = -1/4 (b) x →2 x + x + 2

(d)

lim

(g)

lim

x→2

x→4

x+3

( x − 2)

2

x2 − 9 lim 2 =6/5 x →3 x − x − 6

=5/0=∞=DNE =DNE (e)

x −2 =1/4 x−4

(c)

3x − 5 =3/2 x →∞ 2 x + 4

lim

lim x→2

x+3 =5/0= =5/0=∞=DNE x−2

4x + 7 =0/1=0 x →∞ x − 3 x + 5

(f) lim

2