![blog](https://blog.etrapez.pl/wp-content/uploads/sites/3/2010/09/Granica-funkcji-z-podstawieniem.jpg)
Limit of a Function with Substitution
![](https://blog.etrapez.pl/wp-content/wphb-cache/gravatar/c42/c426df57c11a4502eb4801a4fa1b556fx96.jpg)
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.
Are you looking for college or high school math tutoring? Or maybe you need a course that will prepare you for the final exam?
We are "eTrapez" team. We teach mathematics in a clear, simple and very precise way - we will reach even the most knowledge-resistant students.
We have created video courses translated in an easy, understandable language, which can be downloaded to your computer, tablet or phone. You turn on the video, watch and listen, just like during private lessons. At any time of the day or night.