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 limx⇒0f(x). f(x)=|x|cos⁡x

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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 limx⇒0f(x).  f(x)=|x|cos⁡x

maul124uk · Accepted Answer

Step 1  Given function is  h(x)=xcos⁡1x  we have to find limx⇒0f(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 x⇒0.  h(x)=xcos⁡1x,y1=|x| and y2=−|x|  Since −1≤cos⁡(1x)≤1 for all x≠0  it follows that y2≤h(x)≤y1 for all n≠0  But limx⇒0y2=limx⇒0y1=0  Therefore squeeze theorem can be use to concude that  limx⇒0f(x)=limx⇒0xcos⁡(1x)=0

censoratojk · Accepted Answer

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 &quot;a&quot;.  lima⇒af(x)=limx⇒ah(x)=L  Then, limx⇒ag(x)=L  At x=0,limx⇒0[−|x|]=limx⇒0[|x|]=0  Then, limx⇒0|x|cos⁡(x)=0

nick1337 · Accepted Answer

limx⇒0f(x)=limx⇒0|x| =0.1 limx⇒0f(x)=0

Use a graphing utility to graph the given function and

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