Thursday, September 29, 2016

calculus - Evaluate limit $lim_{x rightarrow 0}left (frac 1x- frac 1{sin x} right )$

Can someone provide me with some hint how to evaluate this limit? $$ \lim_{x \rightarrow 0}\left (\frac 1x- \frac 1{\sin x} \right ) $$ I tried l'hopital's rule but it didn't work.

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analysis - Injection, making bijection

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...