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Math Help - Limits Help

  1. #1
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    Limits Help

    1.) lim as x--> infinity (x - cube root of x)

    2.) lim as x-->0+ ln(2x)


    Anyone know how to solve these limit equations? Thanks.
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  2. #2
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    Quote Originally Posted by sleepiiee View Post
    1.) lim as x--> infinity (x - cube root of x)

    2.) lim as x-->0+ ln(2x)


    Anyone know how to solve these limit equations? Thanks.
    1.) x gets bigger a lot faster than cube root of x .......

    2.) Do you know what the graph of y = ln(2x) looks like .....?
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  3. #3
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    x - x^{\frac{1}{3}} = x^{\frac{1}{3}}(x^{\frac{2}{3}} - 1)

    \lim_{x \to \infty} x^{\frac{1}{3}}(x^{\frac{2}{3}} - 1)

    \lim_{x \to \infty} x^{\frac{1}{3}} \cdot \lim_{x \to \infty} (x^{\frac{2}{3}} - 1)

    finish up


     \lim_{x \to 0^+} \ln(2x)

     \lim_{x \to 0^+} (\ln{x} + \ln{2})

     \lim_{x \to 0^+} \ln{x} + \lim_{x \to 0^+} \ln{2}

    finish up
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  4. #4
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    I got the first one thanks. Still don't understand what to do next with the 2nd problem
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  5. #5
    Super Member 11rdc11's Avatar
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    From the right hand side ln(2x) goes to negative infinity as it approaches 0
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