I want to find $\lim\limits_{x\to\infty}\left(\cos\left(\frac{1}{x}\right)\right)^{\!x}$.I'd like to use the fact that $$\lim_{x\to\infty} e^{\ln(\cos(1/x)^x)}$$but I am not sure what to do after this.
How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...
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