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Math Help - [SOLVED] The Squeeze Theorem

  1. #1
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    [SOLVED] The Squeeze Theorem

    I have an explanation of how to solve this but don't understand one of the steps in it:

    \lim {x\to1} |x-1| \sin^2 x+1



    I don't understand how it follows that 1\leq|x-1|\sin^2 x+1 \leq |x-1|+1
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  2. #2
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    Quote Originally Posted by Mike9182 View Post
    I have an explanation of how to solve this but don't understand one of the steps in it:

    \lim {x\to1} |x-1| \sin^2 x+1



    I don't understand how it follows that 1\leq|x-1|\sin^2 x+1 \leq |x-1|+1
    Since

     <br />
0 \le \sin^2 x \le 1<br />

    then (multiply by |x-1| )


     <br />
0 \le |x-1|\sin^2 x \le |x-1|<br />

    then (add 1)

     <br />
1 \le |x-1|\sin^2 x + 1 \le |x-1| + 1.<br />
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