Polynomial Simplifies to a Number

[hopelynnwelch]

Polynomial Simplifies to a Number, if that even makes sense... lol

\(\displaystyle \displaystyle{ \lim_{h\, \rightarrow\, 0} \,}\) \(\displaystyle \,\dfrac{h^2\, +\, h}{3h^2\, +\, 3h}\)

This reduces to 1/3

Does that mean this limit does not exist?

EDIT*** I think I get this now. The limit is 1/3

 

[stapel]

Polynomial Simplifies to a Number, if that even makes sense... lol

\(\displaystyle \displaystyle{ \lim_{h\, \rightarrow\, 0} \,}\) \(\displaystyle \,\dfrac{h^2\, +\, h}{3h^2\, +\, 3h}\)

This reduces to 1/3

Does that mean this limit does not exist?

EDIT*** I think I get this now. The limit is 1/3

In this particular case, factoring and cancelling does assist in the limit process:

. . . . .\(\displaystyle \dfrac{h^2\, +\, h}{3h^2\, +\, 3h}\, =\, \dfrac{h\,(h\, +\, 1)}{3h\, (h\, +\, 1)}\, =\, \dfrac{h}{3h}\)

The \(\displaystyle \,h\, +\, 1\,\) factors can be cancelled off because, when \(\displaystyle \, h\,\) is close to zero, this factor is well-defined; there are no potential division-by-zero issues. For every value of \(\displaystyle \,h\,\) that is not equal to zero, the remaining variable factors cancel off, too. So the limit, as you get close to (but not equal to) zero, is what's left after the cancellation.

 

[Steven G]

Polynomial Simplifies to a Number, if that even makes sense... lol

\(\displaystyle \displaystyle{ \lim_{h\, \rightarrow\, 0} \,}\) \(\displaystyle \,\dfrac{h^2\, +\, h}{3h^2\, +\, 3h}\)

This reduces to 1/3

Does that mean this limit does not exist?

EDIT*** I think I get this now. The limit is 1/3

Yes, the limit is 1/3

 

[HallsofIvy]

I think someone should point out that this is NOT a polynomial!