Test Question Help

[Obnoxious]

Okay, can someone help me with this little puppy?

$\lim_{x\to0}(\frac{1}{sin x}-\frac{1}{x})$

[Dapthar]

  Quote

Okay' date=' can someone help me with this little puppy?

[math']\lim_{x\to0}(\frac{1}{sin x}-\frac{1}{x})[/math]

Intuitively, as $x\to0$, $sin x \approx x$, therefore, the limit should be $0$.

 

At the moment, I'll just give you a hint. If you combine the two fractions, you get $\lim_{x\to0}{\frac{x-sin x}{x sin x}}$. This is an indeterminate form (namely $\frac{0}{0}$), so you can apply L'Hopital's rule. You'll need to apply it twice, but you'll end up getting that the limit is $0$.

 

If you haven't learned L'Hopital's rule yet, mention so in a post, and I'll try to compute the limit without using it.

[Obnoxious]

I don't wanna post all my steps, but is the answer 0? Please tell me it's 0, as that is what I put on my test.

[Dapthar]

  Obnoxious said:

I don't wanna post all my steps, but is the answer 0?

Yup.

[Dave]

Just a quick hint: To get $\sin(x)$ instead of $sin(x)$, use \sin - looks a lot nicer

[Obnoxious]

Hooray!! I r winnar!