Limits (Algebraically) 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.
Example:
Exercises
Limits and Trigonometry Use your calculator to graph
sin x 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.
Applications:
Find 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.
Proof: -x < xsin(1/x) < x for all x
Since Another example of the squeeze theorem is here.
Other Sites About Limits Weisstein's World of Mathematics
e-mail Questions and Suggestions
|