anonymous
  • anonymous
solve the inequality? x^2e^xlnx>0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[x^2 e^x lnx >0\]
freckles
  • freckles
you only need to solve ln(x)>0
anonymous
  • anonymous
isn't x undefined then?

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freckles
  • freckles
no... \[\ln(x)=y \implies e^{y}=x \\ \text{ here we have } y=0 \\ \text{ so we have } e^{0}=x\] so how do you solve the equation ln(x)=0
freckles
  • freckles
like what is the solution
freckles
  • freckles
and remember y=ln(x) looks like this: |dw:1440878660198:dw|
anonymous
  • anonymous
well e^0 is 1
freckles
  • freckles
drawing got cut off but that line is suppose to be y=0
freckles
  • freckles
so x>1
freckles
  • freckles
x^2e^xln(x)>0 when x>1
anonymous
  • anonymous
so in interval notation, is it \[(1,\infty)\]
freckles
  • freckles
yep
anonymous
  • anonymous
thank you so much
freckles
  • freckles
do you understand how we got that though ?
freckles
  • freckles
|dw:1440878804304:dw|
freckles
  • freckles
e^x was always positive x^2 was always positive ln(x) was going to determine whether or not e^x*x^2*ln(x) was positive or not
anonymous
  • anonymous
yeah, I'm actually kind of mad at myself that I didnt change it to exponential notation.
freckles
  • freckles
just for fun x^2e^xln(x)<0 has solution (0,1)
freckles
  • freckles
I didn't include anything to the left of 0 because ln(x) is undefined there
freckles
  • freckles
left of 0 or 0*
dinamix
  • dinamix
|dw:1440879090764:dw| your graph for function is like that so f(x)>0 in ] 1; +infinity [ @hailbug

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