作业帮lim(2/πarctanx)^x x→∞ lim x^2 e^(1/x^2) x→0 用罗比达求极限.
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lim(2/πarctanx)^x x→∞ lim x^2 e^(1/x^2) x→0 用罗比达求极限.
lim(2/πarctanx)^x x→∞ lim x^2 e^(1/x^2) x→0 用罗比达求极限.
lim(2/πarctanx)^x x→∞ lim x^2 e^(1/x^2) x→0 用罗比达求极限.
lim(2/πarctanx)^x
=lime^[xln(2/πarctanx)]
=lime^{[ln(2/πarctanx)]/(1/x)}
=lime^{[1/(2/πarctanx)*2/π*1/(1+x^2)]/(-1/x^2)}
=lime^{-x^2/[(1+x^2)arctanx]}
=-2/π.
lim x^2 e^(1/x^2)
=lim e^(1/x^2)/(1/x^2)
=lim [e^(1/x^2)*-2/x^3]/(-2/x^3)
=lim e^(1/x^2）
=+∞.
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