若lim x趋向于无穷大 [(x+k)/(x-2k)]^x=e^6,求常数k
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![若lim x趋向于无穷大 [(x+k)/(x-2k)]^x=e^6,求常数k](/uploads/image/z/3936140-44-0.jpg?t=%E8%8B%A5lim+x%E8%B6%8B%E5%90%91%E4%BA%8E%E6%97%A0%E7%A9%B7%E5%A4%A7+%5B%28x%2Bk%29%2F%28x-2k%29%5D%5Ex%3De%5E6%2C%E6%B1%82%E5%B8%B8%E6%95%B0k)
若lim x趋向于无穷大 [(x+k)/(x-2k)]^x=e^6,求常数k
若lim x趋向于无穷大 [(x+k)/(x-2k)]^x=e^6,求常数k
若lim x趋向于无穷大 [(x+k)/(x-2k)]^x=e^6,求常数k
具体见图片.
lim x趋向于无穷大 [(x+k)/(x-2k)]^x
=lim x趋向于无穷大 [(1 +3k/(x-2k)]^{[(x -2k)/3k]*3k+2k}
=lim x趋向于无穷大 [(1 +3k/(x-2k)]^{[(x -2k)/3k]*3k} [(1 +3k/(x-2k)]^(2k)
=e^(3k)=e^6
3k=6
k=2
若lim x趋向于无穷大 [(x+k)/(x-2k)]^x=e^6,求常数k
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