Corollary of Continuity Theorem: Proof

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(Edited)

In this video I go over a simple corollary theorem which is a direct result of the continuity theorem which I went over in my earlier video (video link below). This theorem states that if F, G, and Q are polynomials such that F(x) / Q(x) = G(x) / Q(x) then F = G for all x values even though F/Q is not defined for Q(x) = 0. This is a simple yet important theorem as it simplifies solving the coefficients during partial fraction decomposition.


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Corollary of Continuity Theorem: Proof

Corollary Theorem of Continuity.jpeg

Corollary of Continuity Theorem:

If F, G and Q are polynomials and:

where x is defined everywhere except where Q(x) = 0.

Then F(x) = G(x) for ALL x.

Proof:



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