Help me to solve this problem of limit please?

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1 Answer
Feb 4, 2018

See below.

Explanation:

1) #(1/t+sqrtt/t)(sqrt(t+1)-1)(sqrt(t+1)+1)/(sqrt(t+1)+1)=#
#=1/t(1+sqrtt)t/(sqrt(t+1)+1)=(1+sqrtt)/(sqrt(t+1)+1)#

then

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

10) #x(2-sqrt(4+6/x))((2+sqrt(4+6/x))/(2+sqrt(4+6/x))) =#

#=x(-6/x)/(2+sqrt(4+6/x)) = -6/(2+sqrt(4+6/x))#

then

#lim_(x->oo)x(2-sqrt(4+6/x)) = lim_(x->oo)-6/(2+sqrt(4+6/x))=-3/2#