Limit of a Function with Substitution
Krystian Karczyński
Founder and General Manager of eTrapez.
Graduate of Mathematics at Poznan University of Technology. Mathematics tutor with many years of experience. Creator of the first eTrapez Courses, which have gained immense popularity among students nationwide.
He lives in Szczecin, Poland. He enjoys walks in the woods, beaches and kayaking.
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.
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