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Christos

  • 2 years ago

When a function is not a polynomial?

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

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

  3. hartnn
    • 2 years ago
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    whats the exponent of 'x' ?

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

  5. Christos
    • 2 years ago
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    its 6

  6. Christos
    • 2 years ago
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    why so parthkohli?

  7. hartnn
    • 2 years ago
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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 ?

  8. Christos
    • 2 years ago
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    -6 so its not a polynomial I guess :X

  9. Christos
    • 2 years ago
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    What about the sin(x) ?

  10. hartnn
    • 2 years ago
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    yeah, its not, neither sin x

  11. Christos
    • 2 years ago
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    f(x) = sin(x)

  12. Christos
    • 2 years ago
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    What if the f(x) is a polynomial?

  13. Christos
    • 2 years ago
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    sin(x) = x3-x if I am not mistaken, *confused*

  14. Christos
    • 2 years ago
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    x^3 **

  15. hartnn
    • 2 years ago
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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 ...

  16. Christos
    • 2 years ago
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    hmm what sin(x) is equal to?

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

  18. hartnn
    • 2 years ago
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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.

  19. hartnn
    • 2 years ago
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    cos x = 1-x^2/2!+x^4/4!-x^6/6!+....infinite terms

  20. Christos
    • 2 years ago
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    wait wait what is the notation of "!" used for here?

  21. hartnn
    • 2 years ago
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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

  22. Christos
    • 2 years ago
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    oohhh

  23. Christos
    • 2 years ago
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    thank very much I understand now <3 !

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

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