another limit problem --factoring help??

[sickboy]

The question is : evaluate the lim as x->0 for [(1/t) - (1/(t^2+t))] substitution obviously doesn't work, and I tried to simplify it by cross-multiplying and doing the subtraction, which I don't even know if I'm allowed to do that or not, but that gives (t^2-t+1) / (t^3 + t^2)...which still doesn't work for substitution.. so the bottom part can be factored but can the top be factored also? if so, how?

 

[stapel]

Do you mean the limit statement to be "as x approaches zero" or "as t approaches zero"? Since you don't have an equation across which you can multiply, what are you "cross-multiplying"?

To subtract two fractions, convert to a common denominator. Subtract the numerators. Factor and cancel, if possible.

Eliz.

 

[sickboy]

Oh yeah, it is t->0.. but like i said, i'm having trouble factoring the top term once it's simplified with a common denominator

 

[stapel]

There is nothing to "factor", since there is only just the one term... unless you've made an error in your math. Please reply showing your steps. Thank you.

Eliz.

 

[pka]

He made a huge error in his algebra.
The two terms combine to 1/[t+1] if t≠0.
Since we are finding the limit as t→0, we have t≠0.

 

[stapel]

He made a huge error in his algebra....

I would assume so. And with any luck, he'll reply soon showing his work, and we'll be able to help him correct that error.

Eliz.

 

[soroban]

Hello, sickboy!

Eliz and pka are absolutely correct . . .

Evaluate the lim as t->0 for [(1/t) - (1/(t^2+t))]

.1 . . . 1 . . . . . .1 . . . .1 . . . . . . . . t + 1 . . . . .1 . . . . . . .t + 1 - 1
-- - -------- . = . -- - ---------- . = . ---------- - --------- . = . -----------
.t . .t² + 1 . . . . t . .t(t + 1) . . . . .t(t + 1) . .t(t + 1) . . . . t(t + 1)

Can you finish it now?

 

[sickboy]

Yes! Thanks. I did make an error in my algebra... I see it now. I appreciate the help!

Rob