Question

Lim t->0 (1-(1+t)^2)/t(1+t)^2

Answer 1

-2

Answer 2

can you explain how?

Answer 3

You can't just take the limit for 0/0.
Therefore we need to use a different way (L' Hopital).

Expand and simplify it:
\[\frac{ -t ^{2}-2t }{ t ^{3}+2t ^{2}+t }\]
Take the derivatives of the polynomials:
\[\frac{ -2t-2 }{ 3t ^{2}+4t+1 }\]
Factor and take the limit.

Answer 4

thank you so much

Answer 5

yw