Question

求极限：lim(x趋近-1）ln(2+x)/立方根号下（1+2x)再+1

Answer 1

lim(x→-1）ln(2+x)=0

lim(x→-1）(1+2x)^(1/3) +1=0

罗比达法则

lim(x→-1）ln(2+x)/[(1+2x)^(1/3)+1]

=lim(x→-1）[ln(2+x)]' / [(1+2x)^(1/3)+1]'

=lim(x→-1）[1/(2+x)] /[(2/3) (1+2x)^(-2/3)]

=1/(2/3)

=3/2