# Download Udemy – Calculus 1, part 1 of 2: Limits and continuity 2023-9

## Description

Calculus 1, part 1 of 2: Limits and continuity, the calculus training course: limit and continuity is published by Yudmi Academy. In the first part, you will get a summary of the things you are going to master. You will learn about the structure and properties of the set of real numbers as an ordered string with the complementarity principle, and the results of this definition. The concept of sequence of numbers, with many examples and illustrations; Unique sequences, the definition of a limit of a sequence of numbers, with many examples and illustrations; Mathematical operations on sequences and limit rules for sequences; points of accumulation of sequences; You will learn the concept of continuity of mathematical operations and limit rules for sequences. definite and indefinite forms and their importance; First views on comparison between heights (standard limits at infinity); Cauchy sequences (fundamental sequences) and a scheme of building the set of real numbers using an equivalence relation in the set of all Cauchy sequences with logical elements are among the things you will get to know during the course.

### What you will learn

• How to solve problems related to limit and continuity of functions of one variable and why these methods work.
• The structure and characteristics of the set of real numbers as a regular field with the principle of integrity and the consequences of this definition.
• Supermum, infimum, and redefining the principle of completeness in these expressions.
• numerical sequences and their convergence or divergence; Epsilon definition of the limit of sequences, with illustrations and examples
• Deriving a new limit from an old limit: the limit of the sum, difference, sum, extrapolation, etc., of two sequences with illustrations, formal proofs, and examples.
• The case Squeeze For sequels
• The case Squeeze For functions
• The concept of the finite limit of a function with a real value of a real variable at a point: Cauchy’s definition, Heine’s definition; Proof of their equivalence.
• Limit at infinity and infinite limit of functions: Cauchy’s definition (epsilon-delta) and Heine’s definition (order) of such limits; Their equivalence.

### Who is this course suitable for?

• University and college students who want to learn univariate calculus (or real analysis).
• High school students who are curious about college math.

### Course prerequisites

• “Precalculus 1: Basic notions” (or equivalent): mathematical notation, logic, sets, proofs
• “Precalculus 2: Polynomials and rational functions” (or equivalent)
• “Precalculus 3: Trigonometry” (or equivalent)
• “Precalculus 4: Exponentials and logarithms” (or equivalent)
• You are always welcome with your questions. If something in the lectures is unclear, please, ask. It is best to use QA, so that all the other students can see my additional explanations about the unclear topics. Remember: you are never alone with your doubts, and it is to everyone’s advantage if you ask your questions on the forum.

### Installation guide

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English subtitle

Quality: 720p