Analysis – Complete studies

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Math
● Le espressioni si possono inserire solamente tramite la tastiera dell'app
● Il campo nel quale sarà inserita l'espressione è quello evidenziato in giallo
● Il campo in cui inserire l'espressione si seleziona semplicemente facendo click su di esso. Il campo diventerà così evidenziato in giallo
● Non è possibile comporre parole arbitrarie in quanto inserendo le lettere dell'alfabeto verrà inserito uno spazio dopo di essa per cui ogni lettera sarà riconosciuta come una variabile a se
● Inserendo le varie funzioni predefinite verrà inserito il suo nome e quando si cancella questo elemento verrà cancellato l'intero nome
key C
Cancella l'intera espressione
key CE
Cancella l'ultima espressione inserita
key left arrow
Sposta il cursosre di un'espressione a sinistra
key right arrow
Sposta il cursosre di un'espressione a destra

Complete study of a function

Through the following buttons you can perform a complete study of a function or have the individual parts of the study with more details

Complete study of a function

Study of the domain of a function

Study of the points of discontinuity of a function

Study of the sign of the first derivative


Examples of calculation processes performed by the software (click on the image to see the related development):

Do not enter “y =” but only the expression in x

You can test different input shapes by copying the text in red in the image captions and pasting it into the data entry window that appears by clicking any of the buttons at the top of the page to perform an operation (Complete study of a function, Study of the domain ,etc…).

To enter a piecewise function, see the 4th example below

Study of a fraction goniometric function

Study of a fraction goniometric function (2sin(x)-1)/(1-2cos(x)^2)

Study of a goniometric function

Study of a goniometric function tan(x-Pi/3)^2

Study of a logarithmic function

Study of a logarithmic function
surd(ln(x);3)

Study of a piecewise function

Study of a piecewise function x^2,x<0,sin(x),0<=x<Pi,x^3-x^2,x>=Pi

 

Performance of a function study

The softwareperforms the following operations:

  • Calculation of the domain

  • Graph of the domain and the study of the sign of the function in the Cartesian plane

  • Calculation of the intersections with the Cartesian axes

  • Calculation of limits and asymptotes

  • Calculation of the first derivative and its study of sign for the growth and decrescence

  • Calculation of stationary points based on the study of the sign of the first derivative

  • Calculation of stationary points with the method of subsequent derivatives

  • Calculation of non-derivability points

  • Calculation of the second derivative and its study of sign for the concavity and convexity

  • Calculation of inflection points

  • Calculation of the tangents in the inflection points with an oblique tangent

  • Graph of the function both with a panoramic view without necessarily respecting the proportions on the 2 axes and in detail with the points determined in the previous steps

Example of a sign study of the first derivative

 

Graph of the study of the first derivative sign

Meaning of symbols:

  • Ascending before 0
  • Local maximum in 0
  • Descending between 0 and 1
  • rising point of inflection in 1
  • Descending between 1 and 2
  • Local minimum in 2
  • Ascending after 2

 

 

Example of a sign study of the second derivative:

grafico-studio-segno-derivata-seconda-1

SMeaning of symbols:

  • Concave down before 1-1/√2
  • Inflection point in 1-1/√2
  • Concave up between 1-1/√2 and 1
  • Inflection point in 1
  • Concave down between 1 and 1+1/√2
  • Inflection point in 1+1/√2
  • Concave up after 1+1/√2

Note: time limits for performing calculations

The study of particularly complex functions may not be complete. The system is set to reserve a limited amount of time for performing calculations. 

In this case you will have one of the following situations:

  1. the derivative sign studies will be returned in a simplified form: the relative studies of stationary points and inflection points will not return any results;

Example of a simplified sign study:

studio-di-segno-semplificato

  1. the entire function study will be returned in a reduced form.

Example of a reduced function study:

studio-di-funzione-semplificato

Analysis – Complete studies ultima modifica: 2018-08-31T15:17:07+00:00 da roberto