求极限:lim(x趋近-1)ln(2+x)/立方根号下(1+2x)再+1

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求极限:lim(x趋近-1)ln(2+x)/立方根号下(1+2x)再+1求极限:lim(x趋近-1)ln(2+x)/立方根号下(1+2x)再+1求极限:lim(x趋近-1)ln(2+x)/立方根号下(

求极限:lim(x趋近-1)ln(2+x)/立方根号下(1+2x)再+1
求极限:lim(x趋近-1)ln(2+x)/立方根号下(1+2x)再+1

求极限:lim(x趋近-1)ln(2+x)/立方根号下(1+2x)再+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

洛必达法则求解
lim(x趋近-1)ln(2+x)/立方根号下(1+2x)再+1
=lim(x趋近-1)[1/(2+x)]/[2/3(1+2x)^(-2/3)]
=3/2

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