What is the Limit of a Complex Logarithmic Function in Calculus Homework?

[Kstanley]

Homework Statement

I have this problem on my calculus homework:

$$\lim_{x \to 0} \ln\frac{(\sin(cos(x))(x^5+5x^4+4x^3+17)} {x^6+7x^5+8x^4+9x^3+16})$$

Homework Equations

n/a

The Attempt at a Solution

I honestly have no idea how to go about this. We really haven't been shown anything like this in class, and the complexity of the problem is quite intimidating. I would be grateful for any sort of help.

 

[Char. Limit]

Try evaluating it at x=0 first.

 

[Kstanley]

I got a number like ln.0854, but that was with a calculator which I'm not allowed to use. Not sure how I would do it otherwise

 

[Char. Limit]

Well, every x becomes 0, so your two polynomials reduce to 17 on the top and 16 on the bottom, respectively. Can you see the rest?

 

[Kstanley]

I have this.. is that all? Is there a way I can evaluate sin(1) without a calculator or do I leave as is?

$$<br /> \lim_{x \to 0} \ln\frac{(\sin(1)(17)}{16})<br />$$

 

[Char. Limit]

Yes, you have it in perfectly reduced form.

 

[Kstanley]

That was a lot easier than it looked. I spent so much time trying to make it more complicated then it actually was. Thanks so much for your help.