Use a graphing utility to graph the given function and the equations y=|x| and y=−|x|...
Use a graphing utility to graph the given function and the equations in the same viewing window. Using the graphs to observe the Squeeze Theorem visually, find .
Answer & Explanation
Given function is
we have to find
We know that cosine function is always -1 and is given function is always between and |x| which both go to zero as .
it follows that for all
Therefore squeeze theorem can be use to concude that
Use a graphing utility to graph the given function and the equations
The lower and upper functions have the same limit at .
The middle function has the same limit value because it is trapped between the two outer function.
Suppose for all x in an open interval about "a".