Источник / закреплённая редакция
The Limit of a Function
Источник пакета openstax.calculus_limits · OpenStax Calculus, ch. 2 Limits, module m53491
- work
- urn:openstax:clir:calculus-limits#M53491
- номер
- OpenStax Calculus, ch. 2 Limits, module m53491
- вид
- urn:openstax:clir:calculus-limits#treatise
m53491/index.cnxml at commit 8dbc2ce (main, 2026-07-15)
- edition
- urn:openstax:clir:calculus-limits#M53491_MAIN
- язык
- en
- официальность
- official
- материализация
- PINNED_OFFICIAL_BYTES
- жизненный цикл
- adopted: 2026-07-15
Публикации
| URI | Тип | documentHash | Получено |
|---|---|---|---|
| https://raw.githubusercontent.com/openstax/osbooks-calculus-bundle/8dbc2ce19e804924b2517b89ac72ee45be949d15/modules/m53491/index.cnxml | application/xml; charset=utf-8 | sha256:662325358794c9abe700e4d19e696c801d9eddd4f6c45b918b6185baa9944374 | 2026-09-12T00:00:00Z |
Фрагменты — 2
module/m53491#fs-id1170572479385 · defn · на него ссылаются: 8
en · official · sha256:335229dc4381cc5f878b1e4778bf404e92521fe37a133a060e0d92a01fc80ea1EN
<note id="fs-id1170572479385">
<title>Definition</title>
<para id="fs-id1170572151707">Let <m:math><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow></m:mrow></m:math> be a function defined at all values in an open interval containing <emphasis effect="italics">a</emphasis>, with the possible exception of <emphasis effect="italics">a</emphasis> itself, and let <emphasis effect="italics">L</emphasis> be a real number. If <emphasis effect="italics">all</emphasis> values of the function <m:math><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow></m:mrow></m:math> approach the real number <emphasis effect="italics">L</emphasis> as the values of <m:math><m:mrow><m:mi>x</m:mi><m:mrow><m:mo>(</m:mo><m:mrow><m:mo>≠</m:mo><m:mi>a</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:mrow></m:math> approach the number <emphasis effect="italics">a</emphasis>, then we say that the limit of <m:math><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow></m:mrow></m:math> as <emphasis effect="italics">x</emphasis> approaches <emphasis effect="italics">a</emphasis> is <emphasis effect="italics">L</emphasis>. (More succinct, as <emphasis effect="italics">x</emphasis> gets closer to <emphasis effect="italics">a</emphasis>, <m:math><m:mrow><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow></m:mrow></m:math> gets closer and stays close to <emphasis effect="italics">L</emphasis>.) Symbolically, we express this idea as</para>
<equation id="fs-id1170572133132"><m:math><m:mrow><m:munder><m:mrow><m:mtext>lim</m:mtext></m:mrow><m:mrow><m:mi>x</m:mi><m:mo stretchy="false">→</m:mo><m:mi>a</m:mi></m:mrow></m:munder><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>x</m:mi><m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:mi>L</m:mi><m:mo>.</m:mo></m:mrow></m:math></equation>
</note>Ссылаются нормы: InstructionAvailable, JustifyLimitGiven0, LimitRule, instruction_available, rule_conclusion, rule_method, rule_premise, step_justified_by
module/m53491#fs-id1170571598073 · section · на него ссылаются: 2
en · official · sha256:01e31a2e8ed7fb8095038db67c468616a140edda6ce24345aebb40921676cfa2EN
<link target-id="fs-id1170571598073"/>Ссылаются нормы: JustifyOneSidedAgree15, JustifyOneSidedDiffer16
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