<s>[INST] How do you evaluate this limit? $\ln({x^3+2x^2+x})+ \frac{2}{x}$ How do you evaluate the following?
$$\lim_{x \to 0^+} \left [ \ln({x^3+2x^2+x})+ \frac{2}{x} \right ]$$
If I plug in $x$, I get $\infty-\infty$, which is undetermined, and I haven't been able to get the limit at a more manageable form. Can you please help me?
 [/INST] $\ln(x^3 + 2x^2 + x) + \dfrac{2}{x} = -ln\left(\dfrac{1}{x}\right) + 2\ln(x+1) + \dfrac{2}{x} = \dfrac{1}{x} + 2\ln(x+1) + y\left(1 - \dfrac{lny}{y}\right) \to +\infty$ as $y = \dfrac{1}{x} \to +\infty$ when $x \to 0^+$, and $\dfrac{lny}{y} \to 0$.
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