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

1. ## 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.

2. ## Re: 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.
Yes, it's a typo. What you think is correct.

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

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