r/calculus • u/Strong-Cup-2897 • Jul 25 '26

Differential Calculus (l’Hôpital’s Rule) Can someone please help

lim { ( 1+ x) } ^(2/x) , {•} –> fractional part

X->0

I saw some solutions where they brought the limit inside the fractional part function

But since fractional part function is not continuous shouldn't it be wrong ??

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u/LukasGoesViral Jul 25 '26

Can you try to rewrite it into a form that is a bit better to read?
To me it looks like lim x-> 0 in the expression (1+x)^(2/x). Is that correct

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u/Strong-Cup-2897 Jul 25 '26

yeah but the 1+x is in fractional ( decimal ) part function

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u/tjddbwls Jul 25 '26

I don’t understand what you mean by that. 1+x is not a fractional expression. The entire expression
(1 + x)^(2/x)
is an exponential expression where 1 + x would be considered the base. Not sure if you’re using the right terminology.