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Christos Group Title

When a function is not a polynomial?

  • one year ago
  • one year ago

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  1. Christos Group Title
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    Question: Identify if f(x) = 4 - 2/x^6 is a polynomial and if yes state its degree

    • one year ago
  2. hartnn Group Title
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    when the exponents of the variable are non-negative and integer, the function is polynomial, else not.

    • one year ago
  3. hartnn Group Title
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    whats the exponent of 'x' ?

    • one year ago
  4. ParthKohli Group Title
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    Not to mention, \(\sin(x)\) is not a polynomial either, even if it has a positive exponent.

    • one year ago
  5. Christos Group Title
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    its 6

    • one year ago
  6. Christos Group Title
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    why so parthkohli?

    • one year ago
  7. hartnn Group Title
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    ofcourse, my definition is incomplete , but it suffices in this case. and the term is 2/x^6 which equals, 2x^{-6} now whats the exponent ?

    • one year ago
  8. Christos Group Title
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    -6 so its not a polynomial I guess :X

    • one year ago
  9. Christos Group Title
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    What about the sin(x) ?

    • one year ago
  10. hartnn Group Title
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    yeah, its not, neither sin x

    • one year ago
  11. Christos Group Title
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    f(x) = sin(x)

    • one year ago
  12. Christos Group Title
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    What if the f(x) is a polynomial?

    • one year ago
  13. Christos Group Title
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    sin(x) = x3-x if I am not mistaken, *confused*

    • one year ago
  14. Christos Group Title
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    x^3 **

    • one year ago
  15. hartnn Group Title
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    for polynomial function, exponents of the variable are non-negative and integer example: 1-x^5+x^99 or x^2+x+1 and so on.. sin x is a function of 'x' and no, sin x is not x^3-x ...

    • one year ago
  16. Christos Group Title
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    hmm what sin(x) is equal to?

    • one year ago
  17. Christos Group Title
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    I am doing sin(x) and cos(x) atm they are pretty fresh into my mind :D

    • one year ago
  18. hartnn Group Title
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    sin x = x-x^3/3! +x^5/5!-x^7/7! ....infinite terms for function to be polynomial, the number of terms should be finite. this is the reason why sin x is not a polynomial.

    • one year ago
  19. hartnn Group Title
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    cos x = 1-x^2/2!+x^4/4!-x^6/6!+....infinite terms

    • one year ago
  20. Christos Group Title
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    wait wait what is the notation of "!" used for here?

    • one year ago
  21. hartnn Group Title
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    n! is read as n factorial and is defined as n*(n-1)*(n-2)*...3.2.1 example, 4! = 4*3*2*1

    • one year ago
  22. Christos Group Title
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    oohhh

    • one year ago
  23. Christos Group Title
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    thank very much I understand now <3 !

    • one year ago
  24. hartnn Group Title
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    so you see, sin x and cos x have infinite terms, hence not a polynomial. oh, Welcome ^_^

    • one year ago
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