I have been thinking of this problem recently and am wondering if anyone is able to prove/disprove i

Ryker Stein

Ryker Stein

Answered question

2022-05-26

I have been thinking of this problem recently and am wondering if anyone is able to prove/disprove it:
Let R be a rational function, that is let R ( x ) = p ( x ) / q ( x ) where p and q are polynomials of degree > 0. Assume that at some point x=a, the function R ( x ) is undefined (e.g. by division by zero): That is R ( a )undefined. Then
lim x a R ( x ) = lim x a R ( x ) ,
where R ( x ) = p ( x ) / q ( x ), where p ( x ) and q ( x ) are the derivatives of the polynomials of p and q respectively.
Is this equation always true?

Answer & Explanation

cuprins60

cuprins60

Beginner2022-05-27Added 8 answers

No, it's not:
lim x 0 1 x doesn't exist, yet lim x 0 0 1 = 0
Added after comment below . Still false:
lim x 0 x x 1 x again doesn't exist, yet lim x 0 1 1 = 1

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