Limit of a Function with Substitution

Harder function limits to calculate often require substitution, for example:

Example

The limit in the numerator does not exist, in the denominator it approaches zero… What does the whole thing approach?

A convenient substitution would be:

From the substitution, it follows that:

And that if , then . So we have:

And this limit does not exist, which can be proven in the manner shown in another of my posts.

Krystian Karczyński

Założyciel i szef serwisu eTrapez.

Magister matematyki Politechniki Poznańskiej. Korepetytor matematyki z wieloletnim stażem. Twórca pierwszych Kursów eTrapez, które zdobyły ogromną popularność wśród studentów w całej Polsce.

Mieszka w Szczecinie. Lubi spacery po lesie, plażowanie i kajaki.

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