Calculus problem with limits.

  • Thread starter Kstanley
  • Start date
  • #1
Kstanley
7
0

Homework Statement


I have this problem on my calculus homework:

[tex]
\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})
[/tex]

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.
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,208
22
Try evaluating it at x=0 first.
 
  • #3
Kstanley
7
0
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
 
  • #4
Char. Limit
Gold Member
1,208
22
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?
 
  • #5
Kstanley
7
0
I have this.. is that all? Is there a way I can evaluate sin(1) without a calculator or do I leave as is?

[tex]

\lim_{x \to 0} \ln\frac{(\sin(1)(17)}{16})

[/tex]
 
  • #6
Char. Limit
Gold Member
1,208
22
Yes, you have it in perfectly reduced form.
 
  • #7
Kstanley
7
0
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.
 

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