Trả lời:
Giải bởi Vietjack
b) lim(√n2+2n+3−3√n2+n3)=lim(√n2+2n+3−n)+lim(n−3√n2+n3).
Mà
lim(√n2+2n+3−n)=limn2+2n+3−n2√n2+2n+3+n=lim2+3n√1+2n+3n2+1=21+1=1.
lim(n−3√n2+n3)=limn3−(n2+n3)n2+n.3√n2+n3+(3√n2+n3)2
=lim−11+3√1n+1+(3√1n+1)2=−11+1+1=−13.
Vậy lim(√n2+2n+3−3√n2+n3)=1−13=23.
b) lim(√n2+2n+3−3√n2+n3)=lim(√n2+2n+3−n)+lim(n−3√n2+n3).
Mà
lim(√n2+2n+3−n)=limn2+2n+3−n2√n2+2n+3+n=lim2+3n√1+2n+3n2+1=21+1=1.
lim(n−3√n2+n3)=limn3−(n2+n3)n2+n.3√n2+n3+(3√n2+n3)2
=lim−11+3√1n+1+(3√1n+1)2=−11+1+1=−13.
Vậy lim(√n2+2n+3−3√n2+n3)=1−13=23.
