text: # 微積分-連續性篇 Calculus-Continuity
  
  Free tutorial
  Rating: 4.7 out of 5 (90 ratings)
  1,937 students
  51min of on-demand video
  
  • 先要學習極限的定義與運算
  
  ## Description
  
  ● 函數的連續性在微分學中是非常重要的條件，一個函數可微分的前提就是函數必須要在實數中具有連續的性質，學習微分除了極限外，函數的連續性也是絕對的先修單元。內容包括
  
  1. 連續函數的判斷(Definition of Continuous Functions):
  
  A real value function is continuous if, roughly speaking, the graph is a single unbroken
  curve with no "holes" or "jumps".
  
  2. 中間值定理(The Intermediate Value Theorem):
  
  If a continuous function f with an interval [a, b] as its domain takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.
  
  3. 勘根定理(Bolzano's Theorem) :
  
  If a continuous function has values of opposite sign inside an interval, then it hasat least a root in that interval.
  
  4.漸近線(Asymptotes):
  
  Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph
  
  ● 本課程建議基礎
  
  ●建議完成時間
  
  學習者以二週時間完成
  
  ●教材來源
  
  源於中華科技大學 微積分一 課程中第三單元連續性與第四單元漸近線部分
  
  ●教材認證
  
  內容通過台灣教育部103年度第1梯次數位學習教材認證
  
  ●語言
  
  全部課程繁體中文講授。
  
  ●其他事項
  
  本課程僅供學員自修使用，無法取得中華科技大學學分
  
  ## Who this course is for:
  
  • 對數學有興趣或是有志學好微積分的同學均可適用，若具備高中職數學基本程度在學習上會更加容易。
  
  ## Instructor
  
  • 4.8 Instructor Rating
  • 3,149 Reviews
  • 20,410 Students
  • 11 Courses
explanation: The provided text is a course description for a calculus course focusing on continuity. It outlines the key topics covered, such as the definition of continuous functions, the Intermediate Value Theorem, Bolzano's Theorem, and asymptotes. The text also includes information about the course's rating, duration, prerequisites, and target audience. 
  
  The document does not contain a specific math question or a question and answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 微積分-連續性篇 Calculus-Continuity
  
  Free tutorial
  Rating: 4.7 out of 5 (90 ratings)
  1,937 students
  51min of on-demand video
  
  • 先要學習極限的定義與運算
  
  ## Description
  
  ● 函數的連續性在微分學中是非常重要的條件，一個函數可微分的前提就是函數必須要在實數中具有連續的性質，學習微分除了極限外，函數的連續性也是絕對的先修單元。內容包括
  
  1. 連續函數的判斷(Definition of Continuous Functions):
  
  A real value function is continuous if, roughly speaking, the graph is a single unbroken
  curve with no "holes" or "jumps".
  
  2. 中間值定理(The Intermediate Value Theorem):
  
  If a continuous function f with an interval [a, b] as its domain takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.
  
  3. 勘根定理(Bolzano's Theorem) :
  
  If a continuous function has values of opposite sign inside an interval, then it hasat least a root in that interval.
  
  4.漸近線(Asymptotes):
  
  Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph
  
  ● 本課程建議基礎
  
  ●建議完成時間
  
  學習者以二週時間完成
  
  ●教材來源
  
  源於中華科技大學 微積分一 課程中第三單元連續性與第四單元漸近線部分
  
  ●教材認證
  
  內容通過台灣教育部103年度第1梯次數位學習教材認證
  
  ●語言
  
  全部課程繁體中文講授。
  
  ●其他事項
  
  本課程僅供學員自修使用，無法取得中華科技大學學分
  
  ## Who this course is for:
  
  • 對數學有興趣或是有志學好微積分的同學均可適用，若具備高中職數學基本程度在學習上會更加容易。
  
  ## Instructor
  
  • 4.8 Instructor Rating
  • 3,149 Reviews
  • 20,410 Students
  • 11 Courses
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a course description for a calculus course focusing on continuity. It outlines the key topics covered, such as the definition of continuous functions, the Intermediate Value Theorem, Bolzano's Theorem, and asymptotes. The text also includes information about the course's rating, duration, prerequisites, and target audience. 
  
  The document does not contain a specific math question or a question and answer.
  
  Label: no-question