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

**mathDad** · April 11th 2012, 03:21 PM

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.

**Prove It** · April 11th 2012, 04:41 PM

Originally Posted by mathDad

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.

**mathDad** · April 11th 2012, 04:54 PM

Originally Posted by Prove It

Yes, it's a typo. What you think is correct.

Whew! That's a relief to know. Thanks.

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