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LimitsCalculusCollegeabout 1:27

Find lim x->-infinity e^x: animated lesson

A narrated, step-by-step limits video lesson with captions. Final answer: Limit = 0.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.5 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$\lim_{x \to -\infty} {e}^{x}$
2. Step by step
1. $\lim_{x \to -\infty} {e}^{x} = 0$
  Evaluate the limiting behaviour
2. $\lim_{x \to -\infty} {e}^{x} = 0$
  Identify the value
3. The answer
$\lim_{x \to -\infty} {e}^{x} = 0$
lim x→-∞ e^x = 0
4. Check
- Numerical values as x decreases agree: f(-127.18281) = 0, f(-1271.8281) = 0, f(-12718.281) = 0, f(-127182.81) = 0 ✓

Transcript

The problem. Here is the problem: e to the power x. Find the limit of e to the power x as x → -∞.

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

The answer. So the answer is Limit equals 0. 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.

Check. 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.

About limits

Evaluate limits by substitution, factoring, standard limits and L'Hôpital's rule.

Find lim x->-infinity e^x: Limits Step-by-Step Lesson