Prove the statement using the , definition of a limit lim x 1 1 0 2 x 3 4 Given 0 , we need Select 0 0 such that if 0 x 1 , then 1 0 2 x 3 4 Select But 1 0 2 x 3 4 2 x 2 3 2 3 x 1 x 1 Select ( 3 2 ) 4 4 So if we choose Select 4 ( 3 2 ) 3 2 4 , then 0 x 1 1 0 2 x 3 4 Thus, lim x 1 1 0 2 x 3 4 by the definition of a limit

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Prove the statement using the , definition of a limit   lim x 1 1 0   2 x   3   4 Given   0 , we need       Select         0     0   such that if 0     x 1     , then 1 0   2 x   3 4       Select                 But 1 0   2 x   3 4   2 x 2   3   2   3   x 1       x 1           Select       ( 3   2 ) 4 4   So if we choose         Select       4 ( 3   2 ) 3   2 4 , then 0     x 1     1 0   2 x   3 4     Thus, lim x 1 1 0   2 x   3   4 by the definition of a limit

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Question: Prove the statement using the , definition of a limit . lim x 1 1 0 + 2 x / 3 = 4 Given >

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