Evaluate the Given limit: $\lim _{x \rightarrow-1} \frac{x^{10}+x^{5}+1}{x-1}$
$\lim _{x \rightarrow-1} \frac{x^{10}+x^{5}+1}{x-1}=\frac{(-1)^{10}+(-1)^{5}+1}{-1-1}=\frac{1-1+1}{-2}=-\frac{1}{2}$
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