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Precalculus
Worksheet #3 Limits at Infinity
Name_________________________
Learning Targets:


I can find the limit of a function at infinity.
I can use the limit of a function at infinity to determine the horizontal asymptotes of the
function.
Find the indicated limit.
3x 2  20 x
x  4 x 2  9
1.
lim
x
x  x  9
2.
lim
3.
lim
3x 2  20 x
x  2 x 4  3 x 3  29
4.
lim
5.
lim
7x  9
x  4 x  3
6.
lim
4
x  x  5
9 x2  7
x  5 x  2
7.
9.
2 x5  3x 4  31x
x  8 x 4  31x 2  12
lim
lim
x 
8.
lim
9 x 4  3x  2
4 x3  1
11.
f ( x) 
x 
8x2  7 x
16 x 4  6
Find the horizontal asymptote of the function.
10.
f ( x) 
12.
f ( x) 
2 x 2  3x
8x2  8
36 x 2  7
9x  4
8 x3  x 2
7  11x  4 x 4
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