# Do the Limit Laws Apply to Infinite Limits?

I know that the limit laws state that the limit of a sum, difference, product, and quotient (if the limit of the denominator is not 0) is the [given operator] of the limits. However, I can't seem to prove or find whether this applies with limits that approach infinity.

Could someone verify whether I can apply the limit laws with limits that approach infinity? Thanks.

• Um... I think that 0 times infinity is undefined. This is sort of like the exception to the quotient rule, I think. If the end result is defined, would the laws still sometimes fail? – Jed Dec 9 '15 at 4:11
• Limit laws only apply when all of the limits involved exist (and the example illustrates why it can fail when they don't). – TokenToucan Dec 9 '15 at 4:11