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Math Help - need help plz limits

  1. #1
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    need help plz limits

    need help
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  2. #2
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    Hello, Gracy!

    Are we allowed to use L'Hopital's Rule?


    7. Evaluate: . \lim_{x\to0}\frac{e^x - 1}{x}

    . . (a)\;\infty\qquad(b)\;0\qquad(c)\;1\qquad(d)\;2\qq  uad(e)\text{ limit does not exist}

    The function goes to \frac{0}{0} . . . We can use L'Hopital.

    L'Hopital: . \lim_{x\to0}\frac{e^x}{1}\;=\;\frac{e^0}{1}\;=\;1 . . . answer (c)



    8. Evaluate: . \lim_{x\to\infty}\frac{\ln(x^2)}{x^{\frac{1}{2}}}

    . . (a)\;\infty\qquad(b)\;0\qquad(c)\;2\qquad(3)\text{ limit does not exist}

    The function goes to \frac{\infty}{\infty} . . . We can use L'Hopital.

    We have: . \lim_{x\to\infty}\frac{2\ln(x)}{x^{\frac{1}{2}}}

    L'Hopital: . \lim_{x\to\infty}\frac{2\cdot\frac{1}{x}}{\frac{1}  {2}x^{-\frac{1}{2}}} \;=\;\lim_{x\to\infty}\frac{4}{x^{\frac{1}{2}}} \:=\:0 . . . answer (b)

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