anonymous
  • anonymous
limit as x approaches 5- f(X)= (X-6)/(x-5)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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anonymous
  • anonymous
thats 5 from the negative side, then I have to do 5 from the positive side
hartnn
  • hartnn
you know the meaning of \(5^-\) ?

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anonymous
  • anonymous
yes, its just 5 from the negative side
hartnn
  • hartnn
yeah, specifically that means a number very very near to 5, but less than 5 like 4.99999... you knew this? then what will be x-5 ?
anonymous
  • anonymous
yes but that is just for the denominator if i plug in 5 it will make it zero in the denominator it will make it undefined
hartnn
  • hartnn
thats what the significance of negative sign because it is 5- and not just 5 x-5 will be very small negative number near to 0, and not exactly 0 makes sense ?
anonymous
  • anonymous
I don't understand because the number isnt -5 the number is 5 from the negative side
hartnn
  • hartnn
then you can easily figure out that (negative number)/ (very small negative number) = very large positive number, right ? like (-1)/(0.0000...0009) = very large number
hartnn
  • hartnn
yes, i have not plugged in -5 i have plugged in number very near to 5 but LESS than 5 like 4.999999
hartnn
  • hartnn
because thats what 5\(^-\) means number very near to 5 but LESS than 5
hartnn
  • hartnn
you getting the difference between -5 and 5\(^-\) ?
anonymous
  • anonymous
oh yes i get the difference why you plugged in 4.999 and if it was on the positive side it'd be 5.01
anonymous
  • anonymous
So i still dont know what the limit is
hartnn
  • hartnn
correct! so now can you figure out, what (x-6)/(x-5) will be ?
anonymous
  • anonymous
does that mean it goes to infiniti
hartnn
  • hartnn
yes, but toward which one ? positive or negative infinity ??? can you figure that out ?
anonymous
  • anonymous
I think it will go to positive infiniti because when i plug in the number for the numerator and denominator its negative which changes to positive
anonymous
  • anonymous
and on the positive side 5+ it is negative
anonymous
  • anonymous
right?
hartnn
  • hartnn
lets check! :) 4.99...9- 6 / 4.999..999 -5 = -1/very small negative number = + infinity correct!
anonymous
  • anonymous
does that mean that the limit as x goes to 5 not exist because the negative side is positive infiniti and the positive side is negative infiniti?
hartnn
  • hartnn
5.0001-6/ 5.00001 -5 = -1/ very small positive number = -infinity correct too :)
hartnn
  • hartnn
absolutely correct, for limit to exist, left hand limit must equal right hand limit, which is not the case here
anonymous
  • anonymous
okay great thank you so much
hartnn
  • hartnn
welcome ^_^

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