As the title suggests, I need to prove the $$\lim_{n\rightarrow \infty} n\ln\left(1+\frac{x}{\sqrt{n}}\right)-x\sqrt{n} = \frac{-x^2}{2}$$ I've tried to used things like L'hospitals but to no avail. Any ideas?
I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...
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