Answer:
Why do we want to use l'Hopital's Rule in the first place?
If we try to solve as is we get 0/0, which does nothing for us.
l'Hopital's Rule states:
[tex]\lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]
So take the derivative of the top and bottom and then try to solve
[tex]\frac{cos(x) - 2cos(2x)}{1-cos(x)}[/tex]
Now take the limit at 0
[tex]\frac{cos(0) - 2cos(2(0))}{1-cos(0)}[/tex]
[tex]\frac{1 - 2}{1 - 1} = \frac{1}{0}[/tex]
Since 1-cos(0) = 0, we have to look at values of x close to 0 to see what happens with the curve. This is where a graphing calculator comes in handy. But you can put -1 and 1 into the equation to see what it does.
1 - cos(1) and 1 - cos(-1) will give you negative numbers, so the answer is the limit goes to -∞
Step-by-step explanation:
