Homework #12
Limits at Infinity
Read section 3.1
Exercises from the text: Pages 123-125: #1, #2, #4, #5 a,f,k, #7, #8 b,e, #12
Here are some more exercises in thought and logic that you will most certainly find
interesting.
1.
Suppose that an  diverges to  and Lim f (an )  A . Is it necessarily true that
n 
Lim f ( x )  A ? If not, can you put conditions on either an  and/or f that will
x 
guarantee this result?
2.
Prove: If f has a domain D that is not bounded above and Lim f ( x ) exists and is
x 
finite, then there exists a real number B such that
 f ( x) : x  D
[ B, ) is bounded.