Question

what would be the limit of [(10/x)-(3/x^2)] as x approaches 0?

Answer 1

help

Answer 2

does not exist ?

Answer 3

It looks like negative infinity to me... but the best answer is probably "dne" does not exist.

Answer 4

can you tell me why?

Answer 5

As a denominator approaches zero, the overall fraction gets bigger and bigger.
In your case it is essentially infinity - infinity. The negative infinity has a square on the variable, so it approaches faster... so it looks like negative infinity.
But the wierd thing is that on the negative side, the positive tendency fights the negative, where on the positive side they work together to drive down to infinity. The overall result is that they do not approach at the same rate from the left versus the right, therefore at any given point, they are not equal.
If the limit from the left does not equal the limit from the right, the limit does not exist.

Answer 6

does the answer infinite would be fine?

Answer 7

I don't think so. For the answer to be negative infinity, it has to be the same negative value at any given point x and -x as you approach zero. They never are...

Answer 8

thanks

Answer 9

\[\lim_{x \rightarrow 0^{-}}f(x)=\lim_{x \rightarrow 0^{+}}f(x)\]for the limit to exist... this one is off balance. -1/x^2 is a good example that goes to negative infinity because it is balanced on both sides.

Answer 10

got it

Answer 11

Apply L'Hopital rule

Answer 12

Calculus 2 versus calculus 1

Answer 13

Because it's in the indeterminate form inf - inf

Answer 14

Agreed, a rigorous analytical proof requires L'Hopital's. A graphing method, or table method gets you there roughly for early calculus.

Answer 15

i don't think L'Hospital is allowed for inf-inf.

Answer 16

http://tutorial.math.lamar.edu/Classes/CalcI/LHospitalsRule.aspx

Answer 17

inf-inf can be converted in most cases to the standard inf/inf or 0/0

Answer 18

lol! that reference proves that L'Hospital not applicable for inf-inf, only for 0/0 or inf/inf....u NEED to convert it into any of these forms.....

Answer 19

That's funny... there is no 's' in L'Hopital, but it helps me remember how to spell it too.

Answer 20

what if I just turned it to \[\frac{ 10x-3 }{ x ^{3} }\]?

Answer 21

It is listed in the references alternate indeterminate forms.

Answer 22

just x squared in the denominator, but yes.... then it will be "dne" after one application of L'Hopital's