<s>[INST] Finding the limit as $n \to \infty $ of $n\ln\left(1+\frac{\ x}{n^2}\right)$ Find 

$$\lim_{n\to \infty} n\ln\left(1+\frac{\ x}{n^2}\right)$$ 

My attempt: $\lim_{n\to \infty} n \left[\ln\left(\frac{\ n^2 +x}{n^2}\right)\right]$ 
= $\lim_{n\to \infty} n [\ln (n^2 +x) - \ln(n^2)]$ 
But I'm not sure how to get this out of indeterminate form.
 [/INST] $n\ln\left(1+\frac{\ x}{n^2}\right) = \frac{1}{n}n^2\ln\left(1+\frac{\ x}{n^2}\right) = \frac{1}{n} \ln \left( \left( 1+\frac{x}{n^2} \right)^{n^2} \right)$
If $n\to\infty$, then $ \frac{1}{n} \ln \left( \left( 1+\frac{x}{n^2} \right)^{n^2} \right) \equiv \frac{1}{n} \ln \left( e^x \right) \equiv \frac{x}{n} \equiv 0$
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