<s>[INST] Evaluating $\lim_{x \to 1}\frac{\sin(x^2-x)}{x^2-1}$ and $\lim_{x \to 1}\frac{\ln(x^2+x-1)}{\ln(x^3+x-1)}$ I found these limits and I was unable to solve them due to the occurring indeterminations
$$\lim_{x \to 1}\frac{\sin(x^2-x)}{x^2-1}$$
$$\lim_{x \to 1}\frac{\ln(x^2+x-1)}{\ln(x^3+x-1)}$$
Can someone help me, please?
 [/INST] $$\lim_{x \to 1}\frac{\ln(x^2+x-1)}{\ln(x^3+x-1)} = \lim_{x \to 1} \frac{(2x+1)\cdot(x^3+x-1)}{(3x^2+1)\cdot(x^2+x-1)} = \frac{3}{4}$$ (using L'Hospital)
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