Limits

IrishKnight

Sorry, tis me again, but I promises this will the be that time for a while! (At least I hope!)

Having a bit of bother with this little limit;

lim(x->-2) (2x+5)/(3x^2+4x-4)

When I plug in the number I get 1/0 so I do the following;

lim(x->-2) (2x+5)/(3x-2)(x+2)

From the point on a have no idea what to do...

Pointers?

Fremen

http://en.wikipedia.org/wiki/Limit_%28mathematics%29#l.27H.C3.B4pital.27s_rule

You make a new quotient by differentiating the numerator and differentiating the denominator (NOT by differentiating the whole thing using the quotient rule!)

Then the limit of the new quotient is the same as the limit of the old one.
You can check you're right by substituting in, say, x = -1.99999 in your original formula. If it's close to then answer you got, then you're right.

Michael Collins

That's l'Hopital's Rule you're using there. However I'm not so sure you can use it when you get 1/0 in your answer, only when you get 0/0 or another indeterminate form (e.g. 0^0, 0.infitity, infintiy/infinity etc).

In this case I think the limit just doesn't exist...

LeixlipRed

Yeh Michael is right. It can only be use on indeterminate forms.

EDIT: See here for a list of such forms

Fremen

Michael Collins wrote: »

That's l'Hopital's Rule you're using there. However I'm not so sure you can use it when you get 1/0 in your answer, only when you get 0/0 or another indeterminate form (e.g. 0^0, 0.infitity, infintiy/infinity etc).

In this case I think the limit just doesn't exist...

Whoops, my bad.

LeixlipRed

Fremen wrote: »

Whoops, my bad.

Don't worry about it. Accidentally done the exact same thing many times

Fremen

Heh, in fairness I did say

You can check you're right by substituting in, say, x = -1.99999 in your original formula. If it's close to then answer you got, then you're right.

I was just too lazy to do it myself

Just be glad I'm not designing the next generation of aeroplanes...

LeixlipRed

Fremen wrote: »

Heh, in fairness I did say



I was just too lazy to do it myself

Just be glad I'm not designing the next generation of aeroplanes...

Yeh I'm almost sure I glued the wings on. But I had to rush to the gym....