1.lim x→0 (1+x)^2/sinx 的连续性和极限 2.lim x→1 ( x/(1-x) - 1/lnx )
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1.lim x→0 (1+x)^2/sinx 的连续性和极限 2.lim x→1 ( x/(1-x) - 1/lnx )
1.lim x→0 (1+x)^2/sinx 的连续性和极限 2.lim x→1 ( x/(1-x) - 1/lnx )
1.lim x→0 (1+x)^2/sinx 的连续性和极限 2.lim x→1 ( x/(1-x) - 1/lnx )
1.原式=lim (x-->0)(1+x)^2/x=lim (x-->0)(x+2x+1/x)=无穷大,所以该极限不存在,即在x=0处不连续.
2.首先要知道当x趋于0时ln(1+x)与x是等价无穷小,先令t=x-1,则x=t+1,
则原式=lim(t-->0)((t+1)/(-t)-1/ln(t+1)),
(1)当t正无穷大,-1/ln(t+1)--->正无穷大,整个式子最终--->正无穷大.
(2)当t>0时,同理可得整个式子--->负无穷大.
所以该极限不存在.
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