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Use the Squeeze Theorem to evaluate the limit \( \displaystyle \lim_{x\to 6} f(x)\), if

\(12 x - 36 \leq f(x) \leq x^2 \qquad \textrm{on} \; [4, 8].\)

 

Can someone help to explain this problem and show me how to get the answer?

 Feb 17, 2022
 #1
avatar+122390 
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I barely remember this but I'll take my best shot

 

Note  that    as  x approaches  6, the  function   12x - 36   =  12 (6) - 36  =   72  -36  =    approaches 36

And as x approaches 6, the function x^2  =  6^2 =  approaches  36

 

So.....by the Squeeze Theorem......f(x)  also approaches 36  as x approaches 6  [ i.e., the limit  =36 ] 

 

cool cool cool

 Feb 17, 2022
edited by CPhill  Feb 17, 2022

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