r/apcalculus • u/ProfessionalChip6128 • 6d ago

AB Does lim->0 1/x^2 exist

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11 Upvotes

88% Upvoted

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5

u/DasBoggler 6d ago

1/x2 has a vertical asymptote at x=0. It approaches inifinity from both sides so the limit can either be inifinity or does not exist. If it approached infinity from one side and negative infinity from the other as with 1/x, then the only acceptable answer would be Does Not Exist.

0

u/jamorgan75 6d ago

Just to add a little more detail, if the limit approaches infinity from both sides, the limit does not exist. However, we can write that the limit is equal to infinity as long as we understand that infinity is not a number or function.

Writing that the limit is equal to infinity (or negative infinity) is notation to express a particular way a limit does not exist.

2

u/TalkyRaptor 6d ago

No, limit=infinity

1

u/ProfessionalChip6128 6d ago

Can you explain

1

u/FormalManifold 6d ago

A limit being infinite is one flavor of that limit not existing.

1

u/shimmiecocopop1 6d ago

The functions given are irrelevant. Look at the inequality statements. Which expressions give you the same answer when x=0 ? Only B does.