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高数,求极限问题
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lim(x->2+) e^[1/(x-2)] /[ 1+ e^(2/(x-2)) ]
分子分母同时除 e^(2/(x-2))
=lim(x->2+) { 1/e^[1/(x-2)] } /[ 1/e^(2/(x-2)) +1 ]
=0/(0+1)
=0
lim(x->2-) e^[1/(x-2)] /[ 1+ e^(2/(x-2)) ]
=0/(1+0)
=0
=>
lim(x->2) e^[1/(x-2)] /[ 1+ e^(2/(x-2)) ] =0
分子分母同时除 e^(2/(x-2))
=lim(x->2+) { 1/e^[1/(x-2)] } /[ 1/e^(2/(x-2)) +1 ]
=0/(0+1)
=0
lim(x->2-) e^[1/(x-2)] /[ 1+ e^(2/(x-2)) ]
=0/(1+0)
=0
=>
lim(x->2) e^[1/(x-2)] /[ 1+ e^(2/(x-2)) ] =0
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