Limits with Trigonometric Functions and Polynomials

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Homework Statement



solve the limit:

\lim_{x\rightarrow0}\frac{2cos^{2}(x)-cos(x)-3}{x^{2}}


The Attempt at a Solution



Ok so i factored out the numerator, but i don't know where to go from there any help please.

\lim_{x\rightarrow0}\frac{2cos^{2}(x)-cos(x)-3}{x^{2}}=\lim_{x\rightarrow0}=\frac{(2cos(x)-3)(cos(x)+1)}{x^{2}}
 
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Alright never mind i got limit as x approaches 0 to equal -∞.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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