Direct Substitution for Polynomials - Simple Proof

in MES Science2 years ago

Earlier on I showed what the direct substitution property is and how it can be applied to solve limits involving polynomials or rational functions very easily. In this video I go over a simple proof for the direct substitution property for polynomials using the limit laws, which I have also gone over in my earlier videos. In later videos I will provide precise proofs for all the limit laws used in this video.

Watch video on:

Download video notes:!As32ynv0LoaIiNc5j605e1JCEM6LJg?e=LPkqAy

View Video Notes Below!

Download these notes: Link is in video description.
View these notes as an article:
Subscribe via email:
Donate! :)
Buy MES merchandise!

Reuse of my videos:

  • Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.

Fight back against censorship:

  • Bookmark sites/channels/accounts and check periodically
  • Remember to always archive website pages in case they get deleted/changed.

Buy "Where Did The Towers Go?" by Dr. Judy Wood:
Subscribe to MES Truth:

Join my forums!

Follow along my epic video series:

NOTE #1: If you don't have time to watch this whole video:

Browser extension recommendations:

Direct Substitution for Polynomials: Proof

Direct Substitution Polynomial proof.jpg

Direct Substitution Property

If f is a polynomial or a rational function and ‘a’ is in the domain of f, then:


Functions with the Direct Substitution Property are called continuous at a. Not all limits can be evaluated by direct substitution, such as: