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anonymous

  • 5 years ago

Show that for t>0 logt is not a polynomial.

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  1. amistre64
    • 5 years ago
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    umm.. it doesnt fit the definition of a poly maybe?

  2. anonymous
    • 5 years ago
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    what is the definition of log(t)?

  3. amistre64
    • 5 years ago
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    gotta ask a lumberjack hah!

  4. anonymous
    • 5 years ago
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    has only one zero? hard to know what this question is asking

  5. anonymous
    • 5 years ago
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    amistre i have a question for you. solve for x: 3x+1

  6. anonymous
    • 5 years ago
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    u have o prove that its not a polynomial...thats what given in my book's exercise..

  7. amistre64
    • 5 years ago
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    they always say proving a negative cant be done

  8. anonymous
    • 5 years ago
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    still not sure what it is asking. you need some definition to work with. presumably you are supposed to use some property of the logs that polynomials don't have, but there are so many

  9. amistre64
    • 5 years ago
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    arent logs exponents?

  10. anonymous
    • 5 years ago
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    May be a polynomial is something which has only terms like ax^b

  11. anonymous
    • 5 years ago
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    ln(ab)=ln(a)+ln(b) for example. what polynomial has that property?

  12. anonymous
    • 5 years ago
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    u have to prove it rigourously..

  13. amistre64
    • 5 years ago
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    define rigorous lol

  14. anonymous
    • 5 years ago
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    well you cannot prove it rigorously without appealing to a definition is my guess.

  15. anonymous
    • 5 years ago
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    means the math teacher likes it.

  16. anonymous
    • 5 years ago
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    Yes, you can't say that an apple is red, or is not orange, without defining what red and orange are!

  17. anonymous
    • 5 years ago
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    no polynomial has a vertical asymptote. no polynomial is undefined at 0.

  18. anonymous
    • 5 years ago
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    i said t>0 satellite73

  19. anonymous
    • 5 years ago
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    so? still any asymptote yes? limit as x->0 ln(x) = - infinity

  20. anonymous
    • 5 years ago
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    use this definition:In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

  21. anonymous
    • 5 years ago
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    no poly has that property.

  22. anonymous
    • 5 years ago
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    prove that no polynomial has that property..

  23. anonymous
    • 5 years ago
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    ???

  24. anonymous
    • 5 years ago
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    well its easy

  25. anonymous
    • 5 years ago
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    k. accepted..but would like noncalculus proof..

  26. anonymous
    • 5 years ago
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    the more i think about this the less sense it makes. i am not really sure what it is after. probably something along the lines of "sin(x) is not a polynomial because a polynomial of degree n has at most n real zeros"

  27. anonymous
    • 5 years ago
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    so probably some property of the logs that polynomials do not possess. already suggested ln(ab)=ln(a)+ln(b)

  28. anonymous
    • 5 years ago
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    well deriving from the main definition is the job..

  29. anonymous
    • 5 years ago
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    the book told so..

  30. anonymous
    • 5 years ago
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    i think all the properties will come from the definition.

  31. anonymous
    • 5 years ago
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    but f(xy)=f(x)+f(y) may be true for some polynomials..

  32. anonymous
    • 5 years ago
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    so tat property cant be used!!!

  33. anonymous
    • 5 years ago
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    f(xy)=f(x)+f(y) is not true for any polynomial.

  34. anonymous
    • 5 years ago
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    well f(2x)=constant+f(x) does not hold for any polynomial but with log

  35. watchmath
    • 5 years ago
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    With calculus: Suppose it is equal to some \(p(t)\) then \(\lim_{t\to \infty} \log t/p(t)=1\) On the other hand, by L'hospital rule \(\lim \log t/p(t)=0\)

  36. anonymous
    • 5 years ago
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    @amogh what about the zero polynomials?

  37. anonymous
    • 5 years ago
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    what is with the latex?

  38. anonymous
    • 5 years ago
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    its screwed up...

  39. anonymous
    • 5 years ago
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    I don't think constants come into polynomials, do they?

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