limt→01/〔t√(1+t)〕－1/t

Question

lim【t→0】1/〔t√(1+t)〕－ 1/t

Answer 1

lim 1/(t√(t+1))-1/t
=lim (1-√(t+1))/(t√(t+1))
=lim (1-√(t+1))(1+√(t+1))/(t√(t+1))(1+√(t+1))
=lim (1-t-1)/(t√(t+1))(1+√(t+1))
=lim -t/(t√(t+1))(1+√(t+1))
=lim -1/(√(t+1))(1+√(t+1))
=-1/(1)(1+1)
=-1/2
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