Wolfram alpha in Russian. Wolfram mathematica how to use, tungsten alpha graph online
Basic operations
Examples of- 314+278; 314—278; 314*278; 314^278;
- (a ^ 2 + b ^ 2) + (a ^ 2-b ^ 2); (a ^ 2 + b ^ 2) / (a ^ 2-b ^ 2); (a + b) ^ (2 + 2/3).
Comparison marks
Logical symbols
Basic constants
Main functions
module x: abs (x)
Solving Equations
To get a solution to an equation of the form, it is enough to write in the line Wolfram | Alpha: f [x] = 0, and you will receive some additional information that is generated automatically. If you only need a solution, then you need to enter: Solve = 0, x].
Examples of
- Solve + Cos + Sin = 0, x] or Cos [x] + Cos + Sin = 0;
- Solve or x ^ 5 + x ^ 4 + x + 1 = 0;
- Solve-Log = 0, x] or \ Log-Log = 0.
If your equation contains several variables, then the record: f = 0 will give a very diverse set of information, such as a solution in integers, partial derivatives of a function, etc. To get a solution to an equation of the form in any one of the variables, you need to write in line: Solve = 0, j], where is the variable you are interested in.
Examples of
- Cos = 0 or Solve = 0, x] or Solve = 0, y];
- x ^ 2 + y ^ 2-5 = 0 or Solve or Solve;
- x + y + z + t + p + q = 9.
Solving inequalities
Solving inequalities of the type in Wolfram Alpha is completely analogous to solving an equation. You need to write in the WolframAlpha line: f [x]> 0 or f [x]> = 0 or Solve> 0, x] or Solve> = 0, x].
Examples of
- Cos-1/2> 0 or Solve-1/2> 0, x];
- x ^ 2 + 5x + 10> = 0 or Solve.
If your inequality contains several variables, then writing: f> 0 or f> = 0 will give a very diverse set of information, as in the case of the corresponding equations. To get a solution to this inequality for any one of the variables, you need to write in the line: Solve> 0, j] or Solve> = 0, j], where is the variable you are interested in.
Examples of
- Cos> 0 or Solve> 0, x] or Solve> 0, y];
- x ^ 2 + y ^ 3-5<0 или Solve или Solve;
- x + y + z + t + p + q> = 9.
Solving various systems of equations, inequalities and equations
Solving different kinds of systems in Wolfram Alpha is extremely simple. It is enough to type the equations and inequalities of your system, exactly as described above in paragraphs 7. and 8., connecting them with the union "And", which in Wolfram Alpha has the form &&.
Examples of
- x ^ 3 + y ^ 3 == 9 && x + y = 1;
- x + y + z + p == 1 && x + y-2z + 3p = 2 && x + y-p = -3;
- Sin + Cos == Sqrt / 4 && x + y² = 1;
- Log = 0 && x + y + z<1.
Plotting functions
The Wolfram Alpha service supports the ability to graph both view and view functions. In order to plot a function on a segment, you need to write in the Wolfram Alpha line: Plot, (x, a, b)]. If you want the range of change of the ordinate to be specific, for example, you need to enter: Plot, (x, a, b), (y, c, d)].
Examples of
- Plot;
- Plot;
- Plot ^ x, (x, -Pi, E)];
- Plot ^ x, (x, -Pi, E), (y, 0,1)].
If you need to plot several graphs at once on one figure, then list them using the “AND” union: Plot && g [x] && h [x] &&… && t [x], (x, a, b)].
Examples of
- Plot;
- Plot && Sin && Sin && Sin, (x, -5.5)].
In order to plot a function on a rectangle, you need to write in the Wolfram Alpha line: Plot, (x, a, b), (y, c, d)]. Unfortunately, the range of variation of the applicate cannot be made specific yet. However, it is interesting to note that when you plot a function, you will not only get the surface it defines, but also a "contour map" of the surface (level lines).
Examples of
- Plot, (x, -1, -0.5), (y, -2.2)];
- Plot.
Mathematical analysis
Wolfram Alpha is able to find the limits of functions, sequences, various derivatives, definite and indefinite integrals, solve differential equations and their systems, and much more.
Limits
In order to find the limit of the sequence, you need to write in the line Wolfram Alpha: Limit.
Examples of
- Limit;
- Limit [(1 + 1 / n) ^ n, n -> Infinity].
The limit of the function at can be found in a completely similar way: Limit, x -> a].
Examples of
- Limit / x, x -> 0];
- Limit [(1-x) / (1 + x), x -> −1].
Derivatives
In order to find the derivative of the function, you need to write in the line WolframAlpha: D, x]. If you need to find the derivative of the nth order, then you should write: D, (x, n)]. In the event that you need to find the partial derivative of the function 
write in the gadget window: D, j], where is the variable you are interested in. If you need to find the partial derivative with respect to some variable of order n, then you should enter: D, (j, n)], where means the same as above.
It is important to emphasize that Wolfram Alpha will step by step finding the derivative when you click on “Show Steps” in the upper right corner of its response.
Examples of
- D;
- D;
- D, x];
- D, y],
- D.
Integrals
In order to find the indefinite integral of a function, you need to write in the line WolframAlpha: Integrate f [x], x. Finding a definite integral is just as easy: Integrate, (x, a, b)] or Integrate f (x), x = a..b.
It is important to emphasize that Wolfram Alpha will step by step finding the integral when you click on “Show Steps” in the upper right corner of its answer.
Examples of
- Integrate / x², x];
- Integrate, x];
- Integrate [(x + Sin [x]) / x, (x, 1,100)];
- Integrate / x ^ 5, (x, 1, Infinity)].
Differential equations and their systems
To find the general solution of the differential equation, you need to write in the line WolframAlpha: F (for the kth derivative y, k primes are put).
If you need to solve the Cauchy problem, then write: F, y [s] == A, y "[s] == B, .... should be of the form y [s] == S.
The solution of systems of differential equations is also simple, just write: (f_1, f_2,…, f_n), where f_1, f_2,…, f_n are the differential equations included in the system. Unfortunately, the solution of Cauchy problems and boundary value problems for systems of differential equations is not yet supported.
Examples of
- y "" "+ y" "+ y = Sin [x];
- y "" + y "+ y = ArcSin [x];
- y "" + y + y ^ 2 = 0;
- y "" = y, y == 0, y "= 4;
- y + x * y "= x, y = 2;
- y "" "[x] + 2y" "[x] -3y" [x] + y = x, y = 1, y = 2, y "= 2;
- (x "+ y" = 2, x "-2y" = 4).
Errors when working with the system
The system can make some mistakes when solving complex problems. For example, if you try to solve an inequality, for which you enter the query solve (3x ^ 2-18x + 24) / (2x-2) - (3x-12) / (2x ^ 2-6x + 4)<0, то Wolfram|Alpha выдаст в качестве ответа промежуток , в котором будет присутствовать точка 1, обращающая оба знаменателя исходного неравенства в 0. Так что весь риск и вся ответственность при использовании Wolfram|Alpha ложится на Вас. Скорее всего, данные недочеты будут скоро исправлены.
Factorization
For example, factor
x 2/3 - 3x + 12Let's write as
factor x ^ 2/3 - 3x + 12and press equals (=).
For example, decompose into terms
Let's write as
Partial fraction expansion (1-x ^ 2) / (x ^ 3 + x)
use formulas for the expansion of functions in the Taylor series and the Maclaurin series, or
Series expansion at x = 0
Arrange in a Laurent row:
Laurent expansion z * cos (1 / z) at z = 0
Find the residue of a function at a point:
residue of (e ^ (1 / (1-z ^ 2)) / ((1-e ^ z) * sin (z ^ 2))) at point z = 0
To simplify the expression f [x], type the command Simplify]
Complex conjugate z *
Egyptian fraction:
Egyptian fraction expansion:
Inverse Laplace transform - ILT (find the original from the image)
2 Differential system: (x "= 2x-3y, y" = x-2y + 2sint, x (0) = 0, y (0) = 0) Modulo (-20) mod3 Difference equations f (n + 2) + 2f (n + 1) -8f (n) = 0 The area of the figure bounded by lines: area between y = x ^ 2-x + 1, y = x ^ 3 + 3x ^ 2-2x-1 inverse function y = (x + 6) ^ 3 + 3 - inverse function asymptotes (x (x-3)) / (x + 1) Numerical solution of equations: solve (x ^ 3y "-xy = 1, y (1) = 1) Euler method x = 1..2 solve (x ^ 3y "-xy = 1, y (1) = 1) Runge-Kutta method h = .1 x = 1..2 Integer solution - integer solution An online mathematical processor, a knowledge processor that, at your request, provides data about the world around you in numbers. It all looks very simple - you enter your query in the search field, press the "=" button, you get the result: In fact, WolframAlpha provides free and unlimited access to its knowledge base, which includes a huge amount of information about our world in numerical terms. Demography, economics, history, linguistics, physics, biology, chemistry ... and of course MATHEMATICS - mathematical rules, formulas, algorithms - there is all this, and much, much more. For math students, WolframAlpha is a godsend. This web service easily solves equations and systems, plots functions, calculates limits, finds derivatives, takes integrals ... It looks like it's hard to find a problem that WolframAlpha can't handle. You just need to correctly formulate your request. By the way, although WolframAlpha uses a special syntax, as in other systems of computer mathematics, however, it understands quite well the usual questions asked in ordinary English. For example, you might ask WolframAlpha: “How many students are in Russia now?” Are you wondering what WolframAlpha will answer? How do I use WolframAlpha? A brief description of the service capabilities in Russian is available. To get to know WolframAlpha in detail, and learn more about how to use this service for mathematical calculations, it is worth looking at the only web resource where the mathematical capabilities of WolframAlpha are detailed, accessible and systematically described in Russian - this is the Wolfram | Alpha blog in Russian.
Take a look at how WolframAlpha solves a system of two nonlinear algebraic equations of equations x ^ 2-2y + 1 = 0, x ^ 3 + y ^ 2 = 6: Since the WolframAlpha math engine works on the basis of algorithms from the well-known computer mathematics system Mathametica, these results can be completely trusted. The knowledge base from which WolframAlpha draws its abilities is constantly replenished with relevant materials, factual and numerical data, algorithms - every day WolframAlpha is becoming "smarter"! The capabilities of this system best allow you to evaluate the numerous examples of its use from different fields of knowledge. Among other things, WolframAlpha offers a variety of math products: free widgets for websites, inexpensive mobile math apps for installing on students' smartphones, add-ons and plugins for major browsers, developer tools, and more. For example, for ease of use, you can embed a Wolfram Alpha query box on your site. But if you have already appreciated the capabilities of Wolfram Alpha, then for sure you want to have this tool always at hand. It is enough to install in your browser a suitable extension, toolbar or plug-in from among those offered by the official Wolfram Alpha website. With them, you can turn to Wolfram Alpha at any time. More on this. Recently, WolframAlpha has started using a new math document format - CDF. It is a format that allows you to create documents containing interactive math objects. For example, these can be graphs of functions, differential equations, etc. The user can change the parameters of such objects using the controls built into the document, while simultaneously observing the changes taking place (similar to the GeoGebra Java applets). Based on this format, as well as the Wolfram Alpha widgets, you can, for example, create dynamic illustrations of mathematical rules and algorithms, conduct research, and laboratory classes in mathematics. Get to know Wolfram Alpha immediately if you haven't already! Example 1. To solve the equation x 2 + 3x- 4 = 0, you need to enter solve x ^ 2 + 3x-4 = 0 Example 2. To solve the equation log 3 2 x= 2, you need to enter solve log (3, 2x) = 2 Example 3. To solve equation 25 x-1 = 0.2, you need to enter solve 25 ^ (x-1) = 0.2 Example 4. To solve the equation sin x= 0.5, you need to enter solve sin (x) = 0.5 2. Solution of systems of equations. Example... To solve the system of equations x + y= 5, x — y = 1, you need to enter solve x + y = 5 &&
x-y = 1 Signs &&
3. Solution of rational inequalities of any degree. Example... To solve the inequality x 2 + 3x — 4 < 0, нужно ввести solve x^2+3x-4<0 4. Solution of systems of rational inequalities. Example. To solve the system of inequalities
x 2 + 3x — 4 < 0,
2x 2 — x + 8 > 0, you need to enter solve x ^ 2 + 3x-4<0 &&
2x ^ 2 - x + 8> 0 Signs &&
in this case denotes a logical "AND". 5. Expansion of brackets + casting of similar ones in the expression. Example... To expand the parentheses in the expression ( c + d) 2 (a-c) and bring similar ones, you need enter expand (c + d) ^ 2 * (a-c). 6. Factoring the expression. Example... To factor the expression x 2 + 3x- 4, you need to enter factor x ^ 2 + 3x - 4. 7. Calculation of the amount n the first members of the sequence (including arithmetic and geometric progressions). Example... To calculate the sum of the first 20 terms of the sequence given by the formula a n = n 3 +n, you need to enter sum n ^ 3 + n, n = 1..20 If you need to calculate the sum of the first 10 members arithmetic progression with the first term a 1 = 3, difference d= 5, then you can, as an option, enter a1 = 3, d = 5, sum a1 + d (n-1), n = 1..10 If you need to calculate the sum of the first 7 members geometric progression with the first term b 1 = 3, difference q= 5, then you can, as an option, enter b1 = 3, q = 5, sum b1 * q ^ (n-1), n = 1..7 8. Finding the derivative. Example... To find the derivative of a function f(x) =x 2 + 3x- 4, you need to enter derivative x ^ 2 + 3x - 4 9. Finding the indefinite integral. Example... To find the antiderivative of a function f(x) =x 2 + 3x- 4, you need to enter integrate x ^ 2 + 3x - 4 10. Calculation of a definite integral. Example... To calculate the integral of the function f(x) =x 2 + 3x- 4 on the segment, you need to enter integrate x ^ 2 + 3x - 4, x = 5..7 11. Calculation of limits. Example... To make sure that enter lim (x -> 0) (sin x) / x and see the answer. If you need to calculate some limit at x tending to infinity, one should introduce x -> inf. 12. Research function and plotting. Example... To investigate the function x 3 — 3x 2 and plot it, just enter x ^ 3-3x ^ 2. You will get the roots (the points of intersection with the axis OH), derivative, graph, indefinite integral, extrema. 13. Finding the largest and smallest values of a function on a segment. Example... To find minimal function value x 3 — 3x 2 on the segment, you need to enter minimize (x ^ 3-x ^ 2), (x, 0.5, 2) To find the maximum function value x 3 — 3x 2 on the segment, you need to enter maximize (x ^ 3-x ^ 2), (x, 0.5, 2) A short list of WolframAlpha notation and operators for solving problems online systems of equations and inequalities (lows and highs) Basic commands for Wolfram Alpha 1. Solving equations, building graphs 2. To solve the equation, you just need to enter it For example, x ** 2 + 2x + 1 = 0 3. To plot a graph, you need to use the plot command For example, let's use Tungsten to draw the function 2 ^ (- x) cos (x). This is done with the plot command. From this picture, you can already judge the zeros of the function (solutions to the equation), you can imagine how the function behaves, etc. Better to type in the format To plot several graphs on one coordinate plane (for example, to visualize the solution of systems of equations), with the value of the variable x in the interval (A, B), you need to use the command plot [(f1 [x], f2 (x)), (x, A, B)] For example, the command plot [(2a + 3, a ^ 3-2a ^ 2), (a, -3, Pi] gives such a picture for the intersection of curves 3. To solve the equation "left side (x) = 0", type the command "Solve equation = 0" or, better, in the Solve format ["left side of the equation" == 0, x] Here, the left side is what is on the left in the equation, and zero on the right. Replace "x" with your own variable (y, z, etc.) Example: Solve the equation ax + b = d. Stuffing Solve Getting At the same time, we pressed the button "show steps". To solve a system of equations, use the command Solve [(equation1, equation 2), (variable 1, variable 2)] Example: solve the system of equations 3x + 4y = 0, x * x-y * y = 1 for x, y solve [(3 x + 4 y == 0, x ^ 2-y ^ 2 == 1), (x, y)] To solve the equation in integers, use the "in integers" command. For example: a squared plus b squared equals 25 in whole numbers. 4. To collect factors from a binomial (polynomial) f, type factor [f] 5. To expand the product f into terms, use the expand [f] command 6. To simplify the expression f [x], type the command Simplify] For example, to simplify "e to the power of prearithm x": Simplify [exp [log [x]]] gives the answer x: trainingset = (1-> 1.3.2-> 2.4.3-> 6.4); p = Predict You can classify data. You can not just predict an object, but you can say what a specific value will be equal to. WolframScript can work with files without local kernels using the Wolfram Cloud. Start by creating a text file using the cloud engine. Create a script file called FindPath.wls using the cloud core as an interpreter with the following content. The single function Manipulate gives immediate access to a huge range of powerful interactive capabilities. For any expression with symbolic parameters, Manipulate automatically creates an interface for manipulating the parameters. Manipulate supports not only mouse and keyboard manipulation, but also gamepads and other devices. Only children know what they are looking for. They give all their days to a rag doll, and it becomes very, very dear to them, and if it is taken away from them, the children cry ... LearnPress is a WordPress complete solution for creating a Learning Management System (LMS). It can help you to create courses, lessons and quizzes. #! / usr / local / bin / wolframscript -cloud -print -format PNG samples = ImportString [$ ScriptInputString, "JSON"]; order = Last]; tour = samples []; Show, Graphics]] The script can be executed from the command line using a local text file as input. Edwiser Bridge integrates WordPress with the Moodle LMS. The plugin provides an easy option to import Moodle courses to WordPress and sell them using PayPal. The plugin also allows automatic registration of WordPress users on the Moodle website along with single login credentials for both the systems. NASA will launch an expedition to Mars in July 2020. The spacecraft will deliver to Mars an electronic carrier with the names of all registered members of the expedition. Registration of participants is open. Get your Mars ticket from this link.
One of these code variants must be copied and pasted into the code of your web page, preferably between the tags
This blog is still the only one of this kind, probably also because a competent and complete description of the mathematical capabilities of WolframAlpha is a rather difficult task for students (enthusiasts or moneymakers) (even very good ones!), Who usually take the trouble to host and maintain mathematical resources in Runet. What's more, WolframAlpha's math skills, which start at the most rudimentary, extend too far beyond the standard university math course. I think that they can easily be compared with the mathematical abilities of Stephen Wolfram himself, the developer of the Mathematica system and the mastermind of WolframAlpha.
These abilities are partly illustrated by examples of solving problems from different areas of mathematics posted on the service support site.
1. Solution of rational, fractional-rational equations of any degree, exponential, logarithmic, trigonometric equations.+
addition
—
subtraction
*
multiplication
/
division
^
exponentiation
solve
solution of equations, inequalities,
expand
opening brackets
factor
factorization
sum
calculating the sum of the members of a sequence
derivative
differentiation (derivative)
integrate
integral
lim
limit
inf
Infinity
plot
plot a function
log ( a, b)
logarithm to base a numbers b
sin, cos, tg, ctg
sine, cosine, tangent, cotangent
sqrt
square root
pi
number "pi" (3.1415926535 ...)
e
number "e" (2.718281 ...)
i
Imaginary unit i
minimize, maximize
Finding extrema of a function
We will get the following great picture.
y = 2 a +3
y = a ^ 3 - 2 a ^ 2
in the range from -3 to pi.Wolfram Mathematica Neural Networks 1.0
Wolfram Mathematica Link for Excel 3.1.1
Wolfram classification
WolframScript
Interactive Manipulation
Class 1 |
Overview systemsWolfram MathematicaandWolfram cloud
LearnPress is a WordPress
Video Background Pro now plays video backgrounds
Virtual whiteboards
moodle database organization
Bridge integrates WordPress with the Moodle LMS
If this post solved your problem or you just liked it, share the link to it with your friends on social networks.
The easiest way to connect MathJax is in Blogger or WordPress: in your site's dashboard, add a widget for inserting third-party JavaScript code, copy the first or second version of the loading code presented above into it, and place the widget closer to the beginning of the template (by the way, this is not necessary at all because the MathJax script is loaded asynchronously). That's all. Now, learn the MathML, LaTeX, and ASCIIMathML markup syntax, and you're ready to embed math formulas into your website's web pages.
Another New Year's Eve ... frosty weather and snowflakes on the window pane ... All this prompted me to write again about ... fractals, and what Wolfram Alpha knows about it. There is an interesting article about this, which contains examples of two-dimensional fractal structures. Here we will look at more complex examples of 3D fractals.
A fractal can be visualized (described) as a geometric figure or body (meaning that both are a set, in this case, a set of points), the details of which have the same shape as the original figure itself. That is, it is a self-similar structure, considering the details of which with magnification, we will see the same shape as without magnification. Whereas in the case of a regular geometric shape (not a fractal), when we zoom in, we will see details that have a simpler shape than the original shape itself. For example, at a high enough magnification, part of the ellipse looks like a line segment. This does not happen with fractals: at any increase in them, we will again see the same complex shape, which will repeat over and over again with each increase.
Benoit Mandelbrot, the founder of the science of fractals, wrote in his article Fractals and Art for Science: “Fractals are geometric shapes that are as complex in their details as in their general form. part of the fractal will be enlarged to the size of the whole, it will look like a whole, or exactly, or perhaps with a slight deformation. "
| +
| addition |
| -
| subtraction |
| *
| multiplication |
| /
| division |
| ^
| exponentiation |
| solve | solution of equations, inequalities, systems of equations and inequalities |
| expand | opening brackets |
| factor | factorization |
| sum | calculating the sum of the members of a sequence |
| derivative | differentiation (derivative) |
| integrate | integral |
| lim | limit |
| inf | Infinity |
| plot | plot a function |
| log ( a, b) | logarithm to base a numbers b |
| sin, cos, tg, ctg | sine, cosine, tangent, cotangent |
| sqrt | square root |
| pi | pi (3.1415926535 ...) |
| e | number "e" (2.718281 ...) |
| i | Imaginary unit i |
| minimize, maximize | Finding extrema of a function (minimums and maximums) |
Examples of online problem solving with WolframAlpha
1. Solution of rational, fractional-rational equations of any degree, exponential, logarithmic, trigonometric equations.
Example 1
... To solve the equationx 2
+ 3
x- 4 = 0, you need to entersolve x ^ 2 + 3x-4 = 0
Example2. To solve the equation log 3 2 x = 2
, you need to enter solve log (3, 2x) = 2
Example3. To solve equation 25 x-1 = 0.2, you need to enter solve 25 ^ (x-1) = 0.2
Example4. To solve the equation sin x
= 0.5, you need to enter solve sin (x) = 0.5
2. Solution of systems of equations.
Example... To solve the system of equations
x +
y= 5,
x -
y = 1,
need to enter solve x + y = 5&&
x-y = 1
Signs &&
3. Solution of rational inequalities of any degree.
Example... To solve the inequalityx 2
+ 3
x - 4 < 0, нужно ввести
solve x ^ 2 + 3x-4<0
4. Solution of systems of rational inequalities.
Example.
To solve the system of inequalities
x 2
+ 3
x - 4 < 0,
2
x 2
-
x + 8 > 0,
need to enter solve x ^ 2 + 3x-4<0
&&
2x ^ 2- x + 8 > 0
Signs &&
in this case denotes a logical "AND".
5. Expansion of brackets + casting of similar ones in the expression.
Example
... To expand the parentheses in the expression ( c + d) 2 (a-c) and bring similar ones, you need
enter expand (c + d) ^ 2 * (a-c).
6. Factoring the expression.
Example
... To factor the expressionx 2
+ 3
x- 4, you need to enter factor x ^ 2 + 3x - 4.
7. Calculation of the amount
n
the first members of the sequence (including arithmetic and geometric progressions).
Example
... To calculate the sum of the first 20 terms of the sequence given by the formula a n = n 3 +n, you need to enter sum n ^ 3 + n, n = 1..20
If you need to calculate the sum of the first 10 members arithmetic progression with the first terma
1 = 3, difference d a1 = 3, d = 5, sum a1 + d (n-1), n = 1..10
If you need to calculate the sum of the first 7 members geometric progression with the first termb
1 = 3, difference q= 5, then you can, as an option, enter b1 = 3, q = 5, sum b1 * q ^ (n-1), n = 1..7
8. Finding
derivative.
Example
... To find the derivative of a function f(x) =
x 2
+ 3
x- 4, you need to enter derivative x ^ 2 + 3x - 4
9. Finding
definition of the indefinite integral.
Example
... To find the antiderivative of a function f(x) =
x 2
+ 3
x- 4, you need to enter integratex ^ 2 + 3x - 4
10. Calculation
definite integral.
Example
... To calculate the integral function f(x) =
x 2
+ 3
x- 4 on the segment,
need to enterintegratex ^ 2 + 3x - 4, x = 5..7
11. Calculation
limits.
Example
... To make sure that
enter lim (x -> 0) (sin x) / x and see the answer. If you need to calculate some limit at x tending to infinity, one should introduce x -> inf.
12. Research function and plotting
.
Example
... To investigate the functionx 3
- 3
x 2
and plot it, just enter x ^ 3-3x ^ 2. You will get the roots (the points of intersection with the axis OH), derivative, graph, indefinite integral, extrema.
13. Finding the largest and smallest values of a function on a segment
.
Example
... To find minimal function valuex 3
- 3
x 2
on the segment,
need to enter minimize (x ^ 3-x ^ 2), (x, 0.5, 2)
To find the maximum function valuex 3
- 3
x 2
on the segment,
need to enter maximize (x ^ 3-x ^ 2), (x, 0.5, 2)
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