Limits Infinities and Zeros
It is useful to have the following symbolic fractions when dealing with limits.
Note that infinity means positive or negative infinity.
Limits and Trigonometry
Use your calculator to graph
and discover that
Bye the first theorem, the first fraction approaches 1 as x approaches 0. The second fraction evaluates to zero, hence the total expression is 0.
The Squeeze Theorem
The squeeze theorem says that if a function f is between two functions
that have the same limit, then f has that limit also.
-x < xsin(1/x) < x for all x
Another example of the squeeze theorem is here.
Other Sites About Limits