The science of medals is called. Faleristics - collecting orders, medals, badges
In this project, along with theoretical material and practical. V practical application looked at all sorts of ways to calculate limits. Exploring the second section higher mathematics already arouses great interest, since last year we considered the topic “Matrix. Application of Matrix Properties to Solving Systems of Equations ”, which was simple, if only for the reason that the result was controllable. There is no such control here. The study of the Sections of Higher Mathematics gives its positive result. Classes on this course brought their results: - a large amount of theoretical and practical material; - the ability to choose a method for calculating the limit has been developed; - the competent use of each calculation method has been worked out; - the ability to design a task algorithm has been fixed. We will continue to study the sections of higher mathematics. The purpose of its study is that we will be well prepared for re-studying the course of higher mathematics.
To use the preview of presentations, create yourself a Google account (account) and log into it: https://accounts.google.com
Slide captions:
Calculating the limits of a function. The limit of the function at infinity. Two wonderful limits. Calculation of the number "e". (practical lesson)
The purpose of the lesson: To repeat, summarize and systematize knowledge on the topic "Calculating the limits of a function" and to work out their application in practice
Lesson flow: 1. Organizing time 2. Verification homework 3. Repetition basic knowledge 4. Learning new material 5. Updating knowledge 6. Homework 7. Lesson summary. Reflection
Homework Check Calculate the limits: Option 1 Option 2 1) 1) 2) 2) 3) 3)
Homework check Answers: 1) -1.2; 0.4; -√5 2) 25, 4/3, 1 / 5√2
Repetition of reference knowledge What is called the limit of a function at a point? Write down the definition of the continuity of a function. State the main theorems about limits. What methods of calculating limits do you know?
Repetition of reference knowledge Determination of the limit. The number b is the limit of the function f (x) as x tends to a, if for each positive number e one can specify such positive number d such that for all x different from a and satisfying the inequality | x-a |
Repetition of basic knowledge Basic theorems on limits: THEOREM 1. The limit of the sum of two functions as x tends to a is equal to the sum limits of these functions, that is, THEOREM 2. The limit of the product of two functions as x tends to a is equal to the product of the limits of these functions, that is, THEOREM 3. The limit of the quotient of two functions as x tends to a is equal to the quotient of the limits if the limit of the denominator is nonzero, that is, and is equal to plus (minus) infinity, if the limit of the denominator is 0, and the limit of the numerator is finite and nonzero.
Repetition of basic knowledge Methods for calculating limits: Direct substitution Factoring the numerator and denominator and reducing the fraction Multiplication by conjugates to get rid of irrationality
The study of new material Limit at infinity: The number A is called the limit of the function y = f (x) at infinity (or as x tends to infinity), if for all sufficiently large in modulus values of the argument x, the corresponding values of the function f (x) are arbitrarily small differ from the number A.
Learning new material Divide the numerator and denominator of the fraction n senior degree variable:
Learning new material The first remarkable limit The second remarkable limit is
Learning new material Using wonderful limits First wonderful limit: Second wonderful limit:
Learning new material
Knowledge update
Home Assignment Calculate Limits: Home Assignment
Today I found out ... It was difficult ... It was interesting ... I realized that ... Now I can ... I will try ... I learned ... I was interested ... I was surprised ... Reflection
Loading...