anonymous
  • anonymous
Show that for t>0 logt is not a polynomial.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
umm.. it doesnt fit the definition of a poly maybe?
anonymous
  • anonymous
what is the definition of log(t)?
amistre64
  • amistre64
gotta ask a lumberjack hah!

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anonymous
  • anonymous
has only one zero? hard to know what this question is asking
anonymous
  • anonymous
amistre i have a question for you. solve for x: 3x+1
anonymous
  • anonymous
u have o prove that its not a polynomial...thats what given in my book's exercise..
amistre64
  • amistre64
they always say proving a negative cant be done
anonymous
  • anonymous
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
amistre64
  • amistre64
arent logs exponents?
anonymous
  • anonymous
May be a polynomial is something which has only terms like ax^b
anonymous
  • anonymous
ln(ab)=ln(a)+ln(b) for example. what polynomial has that property?
anonymous
  • anonymous
u have to prove it rigourously..
amistre64
  • amistre64
define rigorous lol
anonymous
  • anonymous
well you cannot prove it rigorously without appealing to a definition is my guess.
anonymous
  • anonymous
means the math teacher likes it.
anonymous
  • anonymous
Yes, you can't say that an apple is red, or is not orange, without defining what red and orange are!
anonymous
  • anonymous
no polynomial has a vertical asymptote. no polynomial is undefined at 0.
anonymous
  • anonymous
i said t>0 satellite73
anonymous
  • anonymous
so? still any asymptote yes? limit as x->0 ln(x) = - infinity
anonymous
  • anonymous
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.
anonymous
  • anonymous
no poly has that property.
anonymous
  • anonymous
prove that no polynomial has that property..
anonymous
  • anonymous
???
anonymous
  • anonymous
well its easy
anonymous
  • anonymous
k. accepted..but would like noncalculus proof..
anonymous
  • anonymous
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"
anonymous
  • anonymous
so probably some property of the logs that polynomials do not possess. already suggested ln(ab)=ln(a)+ln(b)
anonymous
  • anonymous
well deriving from the main definition is the job..
anonymous
  • anonymous
the book told so..
anonymous
  • anonymous
i think all the properties will come from the definition.
anonymous
  • anonymous
but f(xy)=f(x)+f(y) may be true for some polynomials..
anonymous
  • anonymous
so tat property cant be used!!!
anonymous
  • anonymous
f(xy)=f(x)+f(y) is not true for any polynomial.
anonymous
  • anonymous
well f(2x)=constant+f(x) does not hold for any polynomial but with log
watchmath
  • watchmath
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 \(\lim \log t/p(t)=0\)
anonymous
  • anonymous
@amogh what about the zero polynomials?
anonymous
  • anonymous
what is with the latex?
anonymous
  • anonymous
its screwed up...
anonymous
  • anonymous
I don't think constants come into polynomials, do they?

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