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Math Help - stuck on this problem for cal 1

  1. #1
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    stuck on this problem for cal 1

    prove the statement using the epsilison, delta definition of limit:

    limx 3 x/5=3/5


    how would i go about solving this?
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  2. #2
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    \lim_{x \to 3} \frac{x}{5} = \frac{3}{5}

    Going by definition:
    \forall \epsilon > 0, \ \exists \delta > 0 such that whenever 0 < {\color{red}\mid x - 3 \mid} < \delta it follows that \left| \frac{x}{5} - \frac{3}{5} \right| < \epsilon

    Looking at:
    \begin{array}{rcl}\left| \displaystyle \frac{x}{5} - \displaystyle \frac{3}{5} \right| & < & \epsilon \\ \displaystyle \frac{1}{5} {\color{red}\mid x - 3 \mid} & < & \epsilon \\ & \vdots & \end{array}

    It should be clear what you should set \delta to be.
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  3. #3
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    could you offer any tips on proving problems like this. Do you use a method? Anything that can help me grasp this concept would be greatly appreciated.
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  4. #4
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