anonymous
  • anonymous
Solve the inequality x^2e^xln(x)>0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[x ^{2}e ^{x}\ln x>0\]
anonymous
  • anonymous
@FutureMathProfessor
anonymous
  • anonymous
what are the 0's?

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anonymous
  • anonymous
what do you mean by 0's?
anonymous
  • anonymous
what values of x make the left side 0?
anonymous
  • anonymous
if x =0 then the whole left side is 0, and ln 1= 0
anonymous
  • anonymous
also, what is the domain? What values of x are allowed?
anonymous
  • anonymous
including imaginary numbers?
anonymous
  • anonymous
i'd say no...
anonymous
  • anonymous
only real numbers
anonymous
  • anonymous
all real numbers?
anonymous
  • anonymous
nope...
anonymous
  • anonymous
okay so for x^2 all real numbers work, so does e^x , I'm not sure about ln x
anonymous
  • anonymous
break it up... any issues with x^2? any issues with e^x? any issues with ln x?
anonymous
  • anonymous
very good... remember the domain of ln x is x>0
anonymous
  • anonymous
what are the zeros of each of those?
anonymous
  • anonymous
x=0 for x^2 x= 1 for ln x
anonymous
  • anonymous
good. so we can draw a number line and see what happens in the different regions...|dw:1377888075584:dw|
anonymous
  • anonymous
not sure about e^x, I don't think it can equal 0
anonymous
  • anonymous
the signs are for each part and multiplied together tells you whether the function is positive or negative in that interval.
anonymous
  • anonymous
correct, e^x > 0 for all x, x is real
anonymous
  • anonymous
so if x>1 the function is >0 I don't understand the interval between 0-1
anonymous
  • anonymous
x^2 will be positive, as will e^x, but ln x will be negative. when you multiply the signs, it gives you the sign of the number, ex x = 1/2 => (1/2)^2e(1/2)ln(1/2) < 0
anonymous
  • anonymous
@southpaw does this make sense?
anonymous
  • anonymous
err sort of, when nubmers between 0 and 1 are subsituted for x , x^2 is always positive, so is e^x, but ln x will always be negative
anonymous
  • anonymous
so in order for the inequality to be true, x must be greater than 1
anonymous
  • anonymous
exactly
anonymous
  • anonymous
alright thank you!
anonymous
  • anonymous
you're welcome!

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