x趋于0时√(sinx+4)-2⼀ln(x+1)

x趋于0时√(sinx+4)-2/ln(x+1)
2025-12-14 08:25:23
推荐回答(1个)
回答1:

lim(x->0) [√(sinx+4)-2 ]/ln(x+1)
=lim(x->0) [(sinx+4)-4 ]/ { [√(sinx+4)+2 ] .ln(x+1) }
=lim(x->0) sinx/ { [√(sinx+4)+2 ] .ln(x+1) }
=(1/4) lim(x->0) sinx/ ln(x+1)
=(1/4) lim(x->0) x/ x
=1/4