求极限lim(x趋近于2)(ln(x^2-3)/(x^2-3x+2))
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求极限lim(x趋近于2)(ln(x^2-3)/(x^2-3x+2))
lim(x趋近于2)(ln(x^2-3)/(x^2-3x+2))
=lim(x趋近于2)(ln(x^2-4+1)/(x-2)(x-1)
=lim(x趋近于2)[ln(x^2-4+1)^(1/(x-2))]/(x-1)
=lim(x趋近于2)[ln(x^2-4+1)^(1/(x^2-4))*(x+2)]/(x-1)
lim(x趋近于2)[ln(x^2-4+1)^(1/(x^2-4))=e
lim(x趋近于2)(ln(x^2-3)/(x^2-3x+2))=e^4
=lim(x趋近于2)(ln(x^2-4+1)/(x-2)(x-1)
=lim(x趋近于2)[ln(x^2-4+1)^(1/(x-2))]/(x-1)
=lim(x趋近于2)[ln(x^2-4+1)^(1/(x^2-4))*(x+2)]/(x-1)
lim(x趋近于2)[ln(x^2-4+1)^(1/(x^2-4))=e
lim(x趋近于2)(ln(x^2-3)/(x^2-3x+2))=e^4
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