Shown and logarithmic function lesson. Differentiation of display and logarithmic functions - Hypermarket knowledge. IV. Individual robot
Lesson outline
Subject: Algebra
Date: 2.04.13.
Class: 11 class
Teacher: Tishibaeva N.Sh.
Theme: Differentiation by logarithmic i display function... First display function.
meta:
1) formulate the formulas of old logarithmic and display functions; First of all, you know, the first display function
2) development of memory, thrifty, logical thinking, mathematical language of scientists, clearer analysis and development, development of knowledgeable interest to the subject;
3) vikhovuvati community culture of scientists, tips of collective performance, spirovrobitnitstva, mutual assistance.
Lesson type: explanation of new material and consolidation of knowledge, reduction and navichok.
ustatkuvannya : Kartki, interactive board.
technology: differentiation pidhid
Go to lesson:
1.Org. moment. (2xv).
2. Rozgaduvannya crossword puzzle (8min)
1.French mathematician of the 17th century, P'ar Fermat, having designated the whole line as "Straight, most tightly lay down to crooked in the small outskirts of the point."
exact
2. The function is given by the formula y = ah.
show
3.Functions, as given by the formula y = log a x.
logarithmic
4. Derivative change
speed
5. It is called the function F (x) for the function f (x), which is called the word F "(x) = f (x) for any point from interval I.
Pervisna
6. Yak is called the fallowness of the X and Y, when there is a skin element X, it is put at the appearance of a single element of Y.
function
7. If the function f (x) can be represented in the view f (x) = g (t (x)), then this function is called ...
foldable
The word vertically is the name of the French mathematician and mechanics
Lagrange
3.Explanation of the new material: (10 min)
Demonstration function in any point of the region, the designation can be lost and the need to be found for the formula:
(.ln a the formula is replaced by the number and on e, otrimaєmo
(E x) "= e x_ formula lousy exponent
The logarithmic function in any point of the area of the value will be lost, and it will be necessary to follow the formula:
(Log a x) "= the formula has a replaceable number and on e, otrimaєmo
Show function y =(a in any point of the region, the value must be first and foremost for the formula F (x) =+ Z
4. Securing new material (20xv)
Mathematical dictation.
1. Write down the formula for the funky display function (a NS) "
(A x) "= a x · ln a
2. Write down the formula for the funky exponentiality. (e NS) "
(E x) "= e x
3. Write down the formula for the obscene natural logarithm
4. Write down the formula for the common logarithmic function (log a x) "=?
(Log a x) "=
5. Write down zagalny viglyad first for the function f (x) = a NS.
F (x) = + C
6. Write down the primary view of the first for the function:, X ≠ 0. F (x) = ln | x | + Z
Robot bіlya doshki
№255,№256,№258,№259(2,4)
6.D / h # 257, # 261 (2хв)
7. Pidsumok lesson: (3xv)
- What is the formula for the logarithmic function?
What is the formula for setting the display function?
What formula is there a logarithmic function?
What formula is behind the display function
Differentiation by showing i logarithmic functions
1. Number e. Function y = e x, її power, graph, differentiation
Viewable function y \ u003d ax, de a> 1. For the first time, it is possible to recognize the graphs (Fig. 232-234), but it is possible to note that all the stinks pass through the point (0; 1), all the stinks may have a horizontal asymptotic y = 0 at , all the stench of the beast will drop down and, nareshti, all the stench may be similar at all its points. Carried out for the butt to be exact to grafik function y = 2x at point x = 0 (Fig. 232). As soon as you grow up to the point, you can turn over to the one that is close to the point at 35 ° (approx.).
Now we will carry out a dotty graph until the graph of the function y = 3 x also at the point x = 0 (Fig. 233). Here kut mіzh dotichnіy and vіssu х will be more - 48 °. And for the show function y = 10 x in analog
the situation is otrimuєmo kut 66.5 ° (Fig. 234).
Also, as soon as the display function y = ah step by step increases from 2 to 10, then there is a similar function to the graph at the point x = 0 and the abscis step by step increases from 35 ° to 66.5 °. It is logical to respect, that is, for the first time, for which the road is 45 °. The price is based on the number 2 and 3, and for us there are 35 ° for the function, but for us, less than 45 °, and for the function y = 3 x for 48 °, but also more, not more 45 °. To quote us, it is accepted to mean the letter e. It is established that the number e is irrational, so that it is an infinite number of dozens of nonperiodic drib:
e = 2.7182818284590 ...;
in practice, zazvychay vvazhayut, scho e = 2.7.
respect(Not even more serious). It's clear that L.M. Tolstoy doesn’t have anything to say to the number e; Tolstoy.
The graph of the function y = e x images in Fig. 235. The price of the exhibitor, who will be seen from the exhibitors (graphs of displays of their functions with the latest editors), is from the point of view of the graph at the point x = 0 and the list of abscissa of 45 °.
Powerful functions y = e x:
1)
2) not є ni paired, not unpaired;
3) growth;
4) not enclosed at the top, enclosed below;
5) not the least significant, not the least significant;
6) it is not interrupted;
7)
8) tumbled down;
9) differentiated.
Turn to § 45, look at the apparent change of power there by displaying the function y = a x for a> 1. See also power 1-8 (which is completely natural),
Differentiate, I didn’t guess. Negotiated now.
Vivedemo formula for showing obhidnoy y-ex. At the same time, we will not bother with an extravagant algorithm, such as in § 32, and more than once, with success, they were used. At the end of the stage, the algorithm has to calculate the boundary, and the knowledge of the theory between you and me has left and right. To that we will spiral on geometric changes of mind, vazhayuchi, dawn, the very fact of the fact that the function is similar to the graphic display, but not for summing up (for that we have just written down in the induced power the nine-power differentiability = function).
1. Apparently, for the function y = f (x), de f (x) = ex, meaning the same at the point x = 0, we already see: f / = tg45 ° = 1.
2. Introduce the function y = g (x), de g (x) -f (x-a), so that g (x) -Ex "a. In Fig. 236, the graph of the function y = g (x) is shown: vin otrimaniy z the graph of the function y - FX) the deviations along the x axes on | a | unit scale. point x-a is parallel to the dotted graph of the function y = f (x) at the point x -0 (div. fig. 236), which means that I’ll set it up from the top of the x-cut 45 °. vikoristovuchi geometric sense lean, we can write, scho g (a) = tg45 °; = 1.
3. Turn to the function y = f (x). maєmo:
4. We stood up, scho for any meaning and fair spivvidnoshennya. It is possible, naturally, to replace the letter a; Todi Otrimaєmo
From the tsієї of the formula to include a similar formula for integration:
A.G. Mordkovich Algebra 10 class
Calendar-thematic planning in mathematics, video math online, Math in schools download
the lesson lesson outline supporting frame of the presentation to the lesson of the accelerative method of interactive technologies Practice management and right to self-revision by workshops, trainings, casey, home study discussion nutrition rhetorical nutrition from academics іlustratsії audio-, video- and multimedia photographs, pictures, graphics, tables, humor diagrams, anecdotes, jokes, comics parables, orders, crosswords, quotes supplements abstract stats for advanced cheatsheets handwritten basic and supplementary vocabulary Good quality for children and lessonssending pardons to the recipient Updating a fragment in a handbook Elements of innovation at the level of replacing old knowledge with new ones Tilki for readers ideal lessons calendar plan for pik methodical recommendations program negotiation integrated lessonsAlgebra lesson in the 11th grade on the topic: "Differentiation and integration of display and logarithmic functions"
Meta lesson:
Systematization of material, vivcheniy on the theme "Show and logarithmic functions".
Formation of the development of tasks for differentiation and integration of display and logarithmic functions.
vikoristovuvati opportunities information technologies for the development of motivation to the development of folding topics in mathematical analysis.
Viklasta vimogi to vikonannya zalikova robots given by those on the offensive.
Go to lesson
I. organizational moment(1 - 2 chilini).
The teacher will look at the lesson.
Klas breaks into 4 groups.
II. Blitz-experience for formulas (home care).
Conversation in the form of dialogue with scholars.
Supposedly, V paid 10,000 rubles to the bank at a rate of 12% of the money. Do you know how to get along through your rockets?
For all we need virishiti rivnyannya :, tobto Yak?
You need to go to base 10, tobto (with the help of a calculator)
In such a rank, submission to the contribution will be made through a series of rock (small).
Here we knew the formula for the transition to a new basis. And you know what formulas linked to differentiation and integration of logarithmic and display functions? (All the formulas are taken from the side of the handler side 81, p. 86).
Food one by one lancet.
Food for the reader.
The teacher will ask for 1 - 2 formulas.
On some small sheets of paper, there is a mathematical dictation on the knowledge of formulas. Ide mutual check. The elders in the groups are given the arithmetic mean and entered into the table.
Activity table
| Type of business | ||||
| 1. Knowledge of formulas. | ||||
| 2. Individual knowledge. Robot in steam. | ||||
| 3. Sleep of the robot. | ||||
| 4. Control test (evaluation of the computer). | ||||
| 5. Self-operation of the robot(Zavdannya obov'yazkovogo ryvnya). | ||||
| 6. Management of advanced folding. | ||||
III. Sleepy Robot:
Visnuchity number of solutions.
A) 
;
B) 
;
Graphics are displayed on the screen when the scientists behind the additional overhead projector are displayed.
A) 
2 solutions
B) 
1 solution
Dodatkove Pitannya: Know the best function 
The declining function is of the greatest value, if the indicator is of the least value. 
(In 2 ways)
IV. Individual robot.
For an hour, weary robots from a skin group with individual staff working on 2 people.
1 group: One is a useful function, the other is an interactive graphical function.
Dodatkove Pitannya:... View: (Number e? Marvel at the side. 86 handler).
2 group: Know the curve, how to pass through the point n (0; 2), as well as the kutovy function of the dotty in the be-yak point of the crooked road to add the coordinates of the dot to the dot. One warehouse is a differential solution and a bedroom solution, the other is a private solution, when you speak on the cob.
as follows:
Dodatkove Pitannya: what dorivnyu kut similar, carried out at point X = 0 before the graph of the function y = e x і vіssu abscis. (45 o)
I will call the graph of the functional function "the exhibitor" (Know the information about the handler and call your own description with the explanations in the handler page 86).
Group 3:
Adjust
One test is done with the aid of a microcalculator, and the other is without.
Dodatkove Pitannya: Would you like to know if x0 is equal?
as follows: x = 2 0.5.
4 group: Bring it on
Proof in different ways.
Dodatkove Pitannya: Know the value e 1.01. Check your value from the view in butt 2 (side 86 of the handler).
V. Robot with handcuffs.
The lads will get it out and put the butt thinly. 1 - pr. 9 (page 81 - 84 of the handler). Spiral on ci butts, visonati control tests.
Vi. Control tests.
Zavdannya on the screen. Ide negotiation. Vibrate the correct version of the form Computer typeє estimate. The eldest in the group is indicated in the table for the activity of his comrades during the test.
1) the function is given f (x)= 2-e 3x. But, for any value of C, the graph її primary F (x) + С go through the point M (1/3;-e/3)
Suggestion: a) e-1; b) 5/8; c) -2/3; d) 2.
2) the function is given f (x)= E 3x-2 + ln (2x + 3). Know f "(2/3)
View: a) -1; b) 45/13; c) 1/3; d) 2.
3) Chi satisfying function y = e ax rivnyannya y "= ay.
View: a) so; b) dumb; c) all the insult; d) cannot be said for sure.
Vii. Self-defense of the robot.
Head of the obovazkovy level. Find the points to the extremum of the functions.
| III group | |||
The eldest in the group vistavlyaє in the tables of bali for the price of zavdannya.
In a whole hour of skin groups, one person is able to work with small boards with special advanced folding.
| III group | |||
The teacher in the course of showing outside the letter of the design of the building (there is a project on the screen, this is also important for the visitor of the present zalikova robots).
VIII. Homework.
IX. Pidsumok lesson:
Vistavlyannya of assessments from the urahuvannyam of points. Norms of assessments for the maybutny on the offensive level of the robot.
The topic of the lesson: “Differentiation of display and logarithmic functions. The first to show the function "in the staff of UNT
meta : development of theoretical knowledge in science on the topic “Differentiation of display and logarithmic functions. The first to show the function "for the release of the UNT plant.
zavdannya
education: systematize theoretical knowledge of scholarships, secure tips for solving problems with those given.
Developing: development of memory, sparing, logical thinking, mathematical language of scientists, respect, a tool for self-assessment and self-control.
vikhovnі: take:
the formulation in the scientific institutions of the general protégé until the beginning of the day;
development of strong interest in mathematics;
the establishment of positive internal motivation to the development of mathematics.
Metodi navchannya: verbal, practical, practical.
Form robots: Individual, frontal, in pairs.
Go to lesson
Epigraph: "Rozum polyagaє is not only in knowledge, but in clever knowledge in practice" Aristotle (slide 2)
I. Organizational moment.
II. Rozgaduvannya crossword. (Slide 3-21)
The French mathematician of the 17th century P'ar Fermat wrote the whole line as "Straight, most tightly lay down to a crooked point in the small outskirts of the point."
exact
The function is defined by the formula y = log a x.
logarithmic
The function is given by the formula y = a NS.
show
The mathematician of the understanding is victorious at the knowledge of the knowledge of the material point and the cut performance that is similar to the graph of the function in the given point.
lost
It is called the function F (x) for the function f (x), which is called the umov F "(x) = f (x) for any point from interval I.
Pervisna
Yak is called the fallowness of the skin X and Y, when there is a skin element X, it is put at the appearance of a single element of Y.
Moved from change
speed
The function is given by the formula y = e x.
exhibitor
If the function f (x) can be represented in the view f (x) = g (t (x)), then the function is called ...
III. Mathematical dictation. (Slide 22)
1. Write down the formula for the funky display function. ( a x) "= a x ln a
2. Write down the formula of an obscene exponentiality. (E x) "= e x
3. Write down the formula for the obscene natural logarithm. (Ln x) "=
4. Write down the formula for the funky logarithmic function. (log a x) "= 
5. Write down the primary view for the function f (x) = a NS. F (x) = 
6. Write down the primeval view of the first for the function f (x) =, x ≠ 0. F (x) = ln | x | + C
Revise the robot (display on slide 23).
IV. Solution of UNT tasks (simulator)
A) №1,2,3,6,10,36 on preschool and in zoshit (slide 24)
B) Robot in pairs No. 19.28 (simulator) (slide 25-26)
V. 1. Know the pardons: (slide 27)
1) f (x) = 5 e - 3x, f "(x) = - 3 e - 3x
2) f (x) = 17 2x, f "(x) = 17 2x ln17
3) f (x) = log 5
(7x + 1), f "(x) = 
4) f (x) = ln (9 - 4x), f "(x) = 
.
Vi. Presentation of scientists.
Epigraph: "Knowledge is expensive and expensive, so it’s not lousy to add a dzherel" Foma Akvinsky (slide 28)
Vii. House assignment No. 19, 20, part 116
VIII. Test (backup) (slide 29-32)
IX. Pidsumok lesson.
"Yaksho vi want your brother's fate in great life Then remind your head with mathematics, leave є before you can. Wonder to give you some great help in all your life "M. Kalinin (slide 33)
ready robots
DIPLOMA ROBOTS
Bagato is still behind and now I’m a graduate student who will write my diploma robot right away. Ale life is such a thing, that only at once you become zerous, but, having ceased to be a student, you spend all the student joys, many of them, and without having tried, all are appealing and appearing in the middle. And now, instead of the one who needs to do it, the corpus is over the diploma robot? Є awesome wihid: download the need for your diploma robot from our website - and in you it will be a great hour!
Diploma robots were successfully stolen from provincial universities of the Republic of Kazakhstan.
Robotibility from 20 000 tenge
COURSE ROBOTS
Course project - tse persha seriozna practical robot. Itself from the writing of the coursework, preparatory work before the distribution of diploma projects. As soon as the student appears to be right in the wake of those in the course project and competently draw up, then in general they have no problems with the written calls, not with the folds diploma work, Nі z vikonannya іnshih practical buildings... I will help the students with the written type of student robot and grow out of the way of the food, no matter how much it seems, and the information has been distributed.
Robotibility from 2 500 tenge
Master's degree thesis
At the Danish hour principal mortgages Kazakhstan and the country SND widened the steps of the country professional education, Yaka yde for a bachelor's degree - master's degree. At the master's degree, one can start with the idea of rejecting a master's diploma, like becoming a visitor in a large country, not a bachelor's degree, and also becoming foreign robot teachers. Pidsumkom navchannya in magistratury є zahist master's degree dissertation.
We will provide you with relevant analytical and textual material, the part includes 2 scientific statutes and an abstract.
Robotibility from 35 000 tenge
RETURN IN PRACTICE
Writing for any type of student practice (initial, virobnichi, pre-diploma) is required in the area. Tsey document will be approved practical robots student and the basis of the assessment for practice. Make sure that you call on the practice, you need to read and analyze the information about the enterprise, look at the structure and order of the robotics organization, in which practice is carried out, and put the calendar plan and describe your practical work.
In addition, you can write about the practice passing through the specifics of the activity of a particular enterprise.