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Math Help - l'Hospital's Rule: is this a mistake in the book?

  1. #1
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    l'Hospital's Rule: is this a mistake in the book?

    To illustrate l'Hospital's rule, an AP Calculus BC preparation book has the following:


    \lim_{x \rightarrow 0^+}{x^{\sin x}}=\lim_{x \rightarrow 0^+}{e^{x \ln (\sin x)}}

    Say what? I thought x^{\sin x}=e^{\sin x \cdot \ln x}. Is that a typo?
    Thanks.
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  2. #2
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    Re: l'Hospital's Rule: is this a mistake in the book?

    Quote Originally Posted by mathDad View Post
    To illustrate l'Hospital's rule, an AP Calculus BC preparation book has the following:


    \lim_{x \rightarrow 0^+}{x^{\sin x}}=\lim_{x \rightarrow 0^+}{e^{x \ln (\sin x)}}

    Say what? I thought x^{\sin x}=e^{\sin x \cdot \ln x}. Is that a typo?
    Thanks.
    Yes, it's a typo. What you think is correct.
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  3. #3
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    Re: l'Hospital's Rule: is this a mistake in the book?

    Quote Originally Posted by Prove It View Post
    Yes, it's a typo. What you think is correct.
    Whew! That's a relief to know. Thanks.
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