WEBVTT

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Here is the problem: e to the power x.

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Find the limit of e to the power x as x → -∞.

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Evaluate the limiting behaviour. The dominant behaviour of each piece determines the limit.

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Identify the value. The rewritten expression settles to 0, which equals 0 to within 10 to the power minus 6; the converging numerical values below confirm it.

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So the answer is Limit equals 0.

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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 as x decreases agree: f(negative 127.18281) equals 0, f(negative 1271.8281) equals 0, f(negative 12718.281) equals 0, f(negative 127182.81) equals 0, which checks out.