Right Screen 2 for LC B3
Example: Find lim f ( x) if f ( x) 
x 1
x3
.
x 1
1  3 2
 . Since we obtained a number other than
1  1 0
zero in the numerator and the number zero in the denominator, we know
lim f ( x)   , lim f ( x)   , or lim f ( x)  DNE . To determine the answer we
Solution: Notice f (–1) =
x 1
x 1
x 1
need to pick a few values close to –1 on both of its sides and then analyze the
function’s values at these values.

Left side of x = –1 choose x = –1.5 and x = –1.2
1.5  3 1.5
f (1.5) 

 0 (since a positive divided by a negative is a negative)
1.5  1 0.5
1.2  3 1.8
f (1.5) 

 0 (since a positive divided by a negative is a negative)
1.2  1 0.2
Thus, lim f ( x)  
x 1

Right side of x = –1 choose x = –0.5 and x = –0.75
0.5  3 2.5
f (0.5) 

 0 (since a positive divided by a positive is a positive)
0.5  1 0.5
.75  3 2.25
f (0.75) 

 0 (since a positive divided by a positive is a positive)
.75  1 0.25
Thus, lim f ( x)   .
x 1
Since the left and right hand limits are different we conclude lim f ( x)  DNE .
x 1