SOLUTION: How to solve this limit? {{{lim(x->0, (cos(2x) - cos(x))/(0))}}} Please explain Thank you

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Question 1020705: How to solve this limit?
lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%280%29%29
Please explain
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the original limit is
lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%28x%29%29


If so, then here are the steps
Step NumberExpression
1. lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%28x%29%29
2. lim%28x-%3E0%2C+++%282cos%5E2%28x%29+-+1+-+cos%28x%29%29%2F%28x%29%29
3. lim%28x-%3E0%2C+++%282cos%5E2%28x%29+-+cos%28x%29+-+1%29%2F%28x%29%29
4. lim%28x-%3E0%2C+++%28%282cos%28x%29%2B1%29%28cos%28x%29-1%29%29%2F%28x%29%29
5. lim%28x-%3E0%2C+++%282cos%28x%29%2B1%29%2A%28%28%28cos%28x%29-1%29%29%2F%28x%29%29%29
6.
7. lim%28x-%3E0%2C+++%282cos%28x%29%2B1%29%29%2A0
8. %282%2Acos%280%29%2B1%29%2A0
9. %282%2A1%2B1%29%2A0
10. %282%2B1%29%2A0
11. 3%2A0
12. 0


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Notes:

In step 2, I used the trig identity cos%282x%29+=+2cos%5E2%28x%29-1 (see page 2 under "Double Angle Formulas")

In step 6, I broke up the limit using the limit law

In step 7, I used the special trig limit lim%28x-%3E0%2C+++%28%28cos%28x%29-1%29%2Fx%29%29+=+0 (scroll down to bottom half of the page)

From step 8 and beyond, I used the substitution rule and then evaluated/simplified to get the final answer of 0
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So in the end,
lim%28x-%3E0%2C+++%28cos%282x%29+-+cos%28x%29%29%2F%28x%29%29=0

Final Answer: 0