Computer Science and Programming in Python

    SINGLE VARIABLE CALCULUS PART I: DIFFERENTIATION PART A: DEFINITION AND BASIC RULES UNIT 0: LIMITS REVIEW PART 3: Limit of quotients Limit of quotients I. Limit Law for Division    Limits and division                                      Limit Law for Division         If  $$\lim↙{x→a}f(x) = L$$ and  $$\lim↙{x→a}g(x) = M$$ then:     If $M$ ≠$0$ , then $$\lim↙{x→a}{f(x)}/{g(x)} = L/M$$      If $M = 0$ but $L  ≠ 0$, then $$\lim↙{x→a}{f(x)}/{g(x)} = L/M$$ does not exist     If both $M = 0$ and $L = 0$ then $$\lim↙{x→a}{f(x)}/{g(x)} = L/M$$ might exist or not. More work is needed to determine whether the last type of limit exist, and what it is if it does exist. Using the Division Law Infinite Limits Infinite Limits 2

      PYTHON PROGRAMMING   PART II : PYTHON OBJECTS AND DATA STRUCTURE BASICS UNIT 3: STRING PART 2: STRING FORMATTING     In Python, we are having 3 methods to format strings, up to now. They are: - Formatting with placeholders - Formatting with the .format() method - Formatting with Formatted-string (f-string) ( introduced in Python 3.6) I. Formatting with placeholders:        - Use modulo % (string formatting operator)                    print( "Inject %s text here, and %s text here"%('some', 'more' )                         => Inject some text here, and more text here          - You can also pass variables .                   x = 'khiem'                     p...

 ANNOUNCEMENT Sorry guys, due to my final exam, I have not updated any new posts since last week. Tomorrow, I'll be posting new posts again! 

  SINGLE VARIABLE CALCULUS PART I: DIFFERENTIATION PART A: DEFINITION AND BASIC RULES UNIT 0: LIMITS REVIEW PART 2: Continuity I. Definition of continuity at a point     We say that a function $f$    is continuous at a point $x = a$ if     In particular, if $f(a)$ or the limit of $f(x)$ when $x$ approaches $a$ fails, the function is discontinuous at $x = a$.     We say that the function $f$ is right-continuous at point $x = a$ if     Familiarly, we have the left-continuous at point $x = a$ : II. Types of Discontinuities:     There are only two types:         1. If there are a left-hand limit and right-hand limit at point $x = a$, but they are not equal, then we say that there is a jump discontinuity at point $x = a$.         2. If the overall limit of $f(x)$ when x approaches a exists, but $f(a)$ does not equal to that limit, then there is a removable discontin...

                                               PYTHON PROGRAMMING   PART II : PYTHON OBJECTS AND DATA STRUCTURE BASICS UNIT 3: STRING PART I: BASICS OF STRING I. Definition     Strings are used to represent and manipulate a sequence of characters.     Example: "Khiem", "Hello World", "Yesterday, all my trouble seems so far away". II. String basics   1. String indexing and slicing       a) String indexing             We know that strings are sequences of characters so we can use indexes to call parts of the string!                  Let s = "John"                 We have: s[0] = "J"                      ...

SINGLE VARIABLE CALCULUS PART I: DIFFERENTIATION PART A: DEFINITION AND BASIC RULES PART 1: INTRODUCTION TO LIMITS UNIT 0: LIMITS REVIEW I. Definition of left-hand and right-hand side limits                                   Suppose $f(x)$ gets really close to $R$ for values of $x$ that get really close to (but are not equal to) a from the right. Then we say $R$ is the right-hand limit of the function $f(x)$ as x approaches a from the right.           We write:             or Similarly, with $L$ on the left-hand side, we have the left-hand side limit. II. Possible limit behaviors      There are many possible limits to behaviors.           · The right-hand and left-hand limits may both exist and be equal.           · ...