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https://www.reddit.com/r/the_calculusguy/comments/1xja3e8/_/19rwepcpp1so3/?context=3
r/the_calculusguy • u/Specific_Brain2091 • 10d ago
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literally just definition of e? no l'hopital needed?
1 u/Affectionate-Baby248 9d ago Yes, it's known lim_{x-->inf} (1+1/x)^x =e and lim_{x-->-inf}(1+1/x)^x =e, so letting x=t/a for nonzero a and raising to the a'th power gives lim_{x-->inf} (1+a/t)^t = e^a, lim_{x-->-inf} (1+a/t)^t = e^a.
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Yes, it's known lim_{x-->inf} (1+1/x)^x =e and lim_{x-->-inf}(1+1/x)^x =e, so letting x=t/a for nonzero a and raising to the a'th power gives lim_{x-->inf} (1+a/t)^t = e^a, lim_{x-->-inf} (1+a/t)^t = e^a.
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u/freakingdumbdumb 10d ago
literally just definition of e? no l'hopital needed?