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2 3 $$lim_{xtoinfty}left(frac{({e^{1/x}-e^{sin(1/x)})}{x^3}}{{(x!)}^{(1/x)}}right)$$ I have been trying to find the limit of the following sequence above but I am stuck. I first tried using substitution for $sin(1/x)$ because it approaches $0$ ; however, that would make the entire expression $0$ which is obviously wrong. I next tried using the laws of logs, but that just made it more complicated getting nowhere. calculus limits share | cite | improve this question edited yesterday zhw. 71.7k 4 30 75 asked yesterday ...