WEBVTT

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Here is the problem: 1/x squared.

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Find the limit of 1 / x squared as x → 0.

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Nonzero numerator over a denominator approaching 0. The numerator approaches 1 while the denominator approaches 0, so the quotient grows without bound. Its sign on each side decides +∞ or −∞: from the right the quotient → ∞; from the left the quotient → ∞.

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Conclusion. The function is unbounded, so the limit is +∞ (strictly, the limit does not exist as a real number; it diverges to +∞).

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So the answer is Limit equals ∞.

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A limit describes the value a function approaches, not necessarily the value it takes. When substitution gives an indeterminate form, the expression is rewritten (L prime Hôpital prime s rule, a conjugate, or logarithms) until substitution works.

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Numerical values from the right agree: f(0.01) equals 10000, f(0.001) equals 1000000, f(0.0001) equals 100000000, f(0.00001) equals 10000000000, which checks out.

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Numerical values from the left agree: f(negative 0.01) equals 10000, f(negative 0.001) equals 1000000, f(negative 0.0001) equals 100000000, f(negative 0.00001) equals 10000000000, which checks out.