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How to calculate this limit $\lim_{x\to 0}\frac{x^2\sin(1/x)-1}{x^2\ln(1+x^2)-1}$?
I’m trying to calculate the following limit:
$$\lim_{x\to 0}\frac{x^2\sin(1/x)-1}{x^2\ln(1+x^2)-1}=\lim_{x\to 0}\frac{x^2\sin(1/x)}{x^2\ln(1+x^2)}=\lim_{x\to 0}\frac{\sin(1/x)}{x\ln(1+x^2)}.$$
I know that $\lim_{x\to 0}\sin(1/x)=1$, so the limit is actually 1, but how to use it to calculate the limit?
A:
$$\lim_{x\to 0}\frac
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