What is #lim_(trarr0) (1/t -1/(t^2+t)) #?

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Answer 1 · 2015-10-27T22:00:12

#lim_(t->0) (1/t - 1/(t^2+t)) = 1#

#1/t - 1/(t^2+t) = (t+1)/(t^2+t) - 1/(t^2+t) = t/(t(t+1)) = 1/(t+1)#

with exclusion #t != 0#

So

#lim_(t->0) (1/t - 1/(t^2+t)) = lim_(t->0) (1/(t+1)) = 1/1 = 1#

Answer 2 · 2015-10-27T22:01:35

It is

#lim_(trarr0) (1/t -1/(t^2+t))=lim_(trarr0) (t^2+t-t)/(t^2(t+1))=lim_(trarr0) 1/(t+1)=1#