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    [id] => 7186
    [paper_index] => 202206-01-010642
    [title] => INVARIANT DEFINITION OF A TANGENT 
    [description] => 
    [author] => Eshbekov Raykhonbek,Abdurakhmanov Bobomurod G'ulombek ugli
    [googlescholar] => https://scholar.google.co.in/scholar?q=eprajournals.com&hl=en&scisbd=2&as_sdt=0,5
    [doi] => 
    [year] => 2022
    [month] => June
    [volume] => 8
    [issue] => 6
    [file] => 812pm_43.EPRA JOURNALS 10642.pdf
    [abstract] => When forming and describing mathematical concepts, its definition is of great importance.
It is known that the concept of a tangent to the graph of functions and to any curves is important in mathematics.
But the very introduction or definition of a tangent requires special attention.
The purpose of our study is to introduce the concept of a tangent for graphically defined functions without applying the concepts of the derivative and secant line. We know that any function can be defined analytically, graphically, and tabularly.
 First consider the logical requirement for introducing and describing the definition of the concepts to be introduced.

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    [doj] => 2022-06-22
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    [status] => y
    [award_status] => P
    [orderr] => 43
    [journal_id] => 1
    [googlesearch_link] => 
    [edit_on] => 
    [is_status] => 1
    [journalname] => EPRA International Journal of Multidisciplinary Research (IJMR)
    [short_code] => IJMR
    [eissn] =>  2455-3662 (Online)
    [pissn] => - --
    [home_page_wrapper] => images/products_image/11.IJMR.png
)
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