Christos
When a function is not a polynomial?
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Christos
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Question: Identify if f(x) = 4 - 2/x^6 is a polynomial and if yes state its degree
hartnn
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when the exponents of the variable are non-negative and integer, the function is polynomial, else not.
hartnn
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whats the exponent of 'x' ?
ParthKohli
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Not to mention, \(\sin(x)\) is not a polynomial either, even if it has a positive exponent.
Christos
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its 6
Christos
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why so parthkohli?
hartnn
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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 ?
Christos
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-6 so its not a polynomial I guess :X
Christos
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What about the sin(x) ?
hartnn
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yeah, its not, neither sin x
Christos
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f(x) = sin(x)
Christos
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What if the f(x) is a polynomial?
Christos
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sin(x) = x3-x if I am not mistaken, *confused*
Christos
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x^3 **
hartnn
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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 ...
Christos
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hmm what sin(x) is equal to?
Christos
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I am doing sin(x) and cos(x) atm they are pretty fresh into my mind :D
hartnn
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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.
hartnn
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cos x = 1-x^2/2!+x^4/4!-x^6/6!+....infinite terms
Christos
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wait wait what is the notation of "!" used for here?
hartnn
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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
Christos
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oohhh
Christos
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thank very much I understand now <3 !
hartnn
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so you see, sin x and cos x have infinite terms, hence not a polynomial.
oh, Welcome ^_^