I can't find a way to continue with this calculation of limit: <munder> <mo form="prefix">li

meindwrhc

meindwrhc

Answered question

2022-05-22

I can't find a way to continue with this calculation of limit:
lim x ( π 2 arctan ( x ) ) 1 ln ( x ) = lim x e ln ( π 2 arctan ( x ) ) ln ( x ) .

Answer & Explanation

pelankp

pelankp

Beginner2022-05-23Added 8 answers

With y := 1 / x this becomes
exp ( lim y 0 + ln arctan y ln y ) = exp ( lim y 0 + 1 arctan y 1 1 + y 2 1 y ) = exp ( lim y 0 + y arctan y ) = 1 e ,
because lim y 0 + 1 1 + y 2 = 1

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