anonymous
  • anonymous
OKAY. So I need help with how to do this question. I'm not sure how they got the answer in the book, and I must be doing something wrong in the denominator. I'll draw it out below.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1449798427904:dw|
anonymous
  • anonymous
\[\lim_{x \rightarrow 0} (3\sin x +\cos x-1)/4x)\]
HELP!!!!
  • HELP!!!!
Check out this calculator that shows the everything step by step https://www.symbolab.com/

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anonymous
  • anonymous
@HELP!!!! It says the input is not valid. Honestly, I just need someone to explain where I'm going wrong and that calculator isn't helping.
anonymous
  • anonymous
@jim_thompson5910 Any help?
jim_thompson5910
  • jim_thompson5910
@Outh-1 did you try breaking up the fraction? \[\Large \lim_{x \to 0}\left[\frac{3\sin(x)+\cos(x)-1}{4x}\right]\] \[\Large \lim_{x \to 0}\left[\frac{3\sin(x)}{4x}+\frac{\cos(x)-1}{4x}\right]\] \[\Large \lim_{x \to 0}\left[\frac{3\sin(x)}{4x}\right]+\lim_{x \to 0}\left[\frac{\cos(x)-1}{4x}\right]\] \[\Large \frac{3}{4}\lim_{x \to 0}\left[\frac{\sin(x)}{x}\right]+\frac{1}{4}\lim_{x \to 0}\left[\frac{\cos(x)-1}{x}\right]\]
jim_thompson5910
  • jim_thompson5910
let me know if that helps or not
jim_thompson5910
  • jim_thompson5910
you'll finish up by using these special limits http://www.lchr.org/a/36/oi/Triglim.jpg
jim_thompson5910
  • jim_thompson5910
oh nearly forgot, but keep in mind that cos(x) - 1 = -[ 1-cos(x) ]
anonymous
  • anonymous
I was unaware that you could take the 3/4 and 1/4 out of the brackets and could put it outside(?) of the limit. You are putting it outside, correct? @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
yes, I'm using the rule \[\Large \lim_{x \to a}\left[k*f(x)\right] = k*\lim_{x \to a}\left[f(x)\right]\] where k is some fixed constant
jim_thompson5910
  • jim_thompson5910
they are outside the limit
anonymous
  • anonymous
Neato. I got the right answer. I'll have to remember that for my final next week. Thanks a lot! @jim_thompson5910
jim_thompson5910
  • jim_thompson5910
you're welcome

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