Prove the statement using the , definition of a limit lim x 4 ( x 2 6 ) 1 0 Given 0 , we need such that if 0 x ( 4 ) , then ( x 2 6 ) 1 0 whenever 0 x 4 Notice that if x 4 1 , then 1 9 x 4 0 x 4 x 4 9 and x 4 9 , so ( x 2 6 ) 1 0 ( x 4 ) ( x 4 ) x 4 x 4 ( 9 ) ( 9 ) or upon simplifying we need x 2 1 6 limit , lim x 4 ( x 2 6 ) q , So take min 9 , 1 Then Thus, by the definition of a

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Prove the statement using the , definition of a limit   lim x   4 ( x 2   6 )   1 0 Given   0 , we need such that if 0   x   (   4 )   , then   ( x 2   6 )   1 0   whenever 0   x   4     Notice that if   x   4   1 , then   1   9   x   4         0   x   4         x   4   9 and   x   4   9 , so   ( x 2   6 )   1 0       ( x   4 ) ( x   4 )       x   4     x   4   ( 9 ) ( 9 )   or upon simplifying we need   x 2   1 6   limit , lim x   4 ( x 2   6 )   q , So take   min   9 , 1     Then Thus, by the definition of a

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Question: Prove the statement using the , definition of a limit . lim x - 4 ( x 2 - 6 ) = 1 0 Given

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