Use a graphing utility to graph the given function and the equations y=|x| and y=−|x|...

Joseph Krupa

Joseph Krupa

Answered

2021-12-18

Use a graphing utility to graph the given function and the equations y=|x| and y=|x| in the same viewing window. Using the graphs to observe the Squeeze Theorem visually, find limx0f(x).
f(x)=|x|cosx

Answer & Explanation

maul124uk

maul124uk

Expert

2021-12-19Added 35 answers

Step 1
Given function is
h(x)=xcos1x
we have to find limx0f(x)
Step 2
We know that cosine function is always -1 and is given function is always between |x| and |x| which both go to zero as x0.
h(x)=xcos1x,y1=|x| and y2=|x|
Since 1cos(1x)1 for all x0
it follows that y2h(x)y1 for all n0
But limx0y2=limx0y1=0
Therefore squeeze theorem can be use to concude that
limx0f(x)=limx0xcos(1x)=0
censoratojk

censoratojk

Expert

2021-12-20Added 46 answers

Step 1
Given:
f(x)=|x|cos(x)
Use a graphing utility to graph the given function and the equations
y=|x|
and y=|x|
Step 2
Explanation:
The lower and upper functions have the same limit at x=0.
The middle function has the same limit value because it is trapped between the two outer function.
Step 3
Squeez Theorem:
Suppose f(x)g(x)h(x) for all x in an open interval about "a".
limaaf(x)=limxah(x)=L
Then, limxag(x)=L
At x=0,limx0[|x|]=limx0[|x|]=0
Then, limx0|x|cos(x)=0
nick1337

nick1337

Expert

2021-12-28Added 573 answers

limx0f(x)=limx0|x|
=0.1
limx0f(x)=0

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?