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thats 5 from the negative side, then I have to do 5 from the positive side
you know the meaning of \(5^-\) ?
yes, its just 5 from the negative side
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 ?
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
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 ?
I don't understand because the number isnt -5 the number is 5 from the negative side
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
yes, i have not plugged in -5 i have plugged in number very near to 5 but LESS than 5 like 4.999999
because thats what 5\(^-\) means number very near to 5 but LESS than 5
you getting the difference between -5 and 5\(^-\) ?
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
So i still dont know what the limit is
correct! so now can you figure out, what (x-6)/(x-5) will be ?
does that mean it goes to infiniti
yes, but toward which one ? positive or negative infinity ??? can you figure that out ?
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
and on the positive side 5+ it is negative
lets check! :) 4.99...9- 6 / 4.999..999 -5 = -1/very small negative number = + infinity correct!
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?
5.0001-6/ 5.00001 -5 = -1/ very small positive number = -infinity correct too :)
absolutely correct, for limit to exist, left hand limit must equal right hand limit, which is not the case here
okay great thank you so much