求极限.lim(x→无穷)[(2ˆ(1∕x)+3ˆ(1∕x))∕2]ˆx
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求极限.lim(x→无穷)[(2ˆ(1∕x)+3ˆ(1∕x))∕2]ˆx
求极限.lim(x→无穷)[(2ˆ(1∕x)+3ˆ(1∕x))∕2]ˆx
求极限.lim(x→无穷)[(2ˆ(1∕x)+3ˆ(1∕x))∕2]ˆx
lim ln[(2ˆ(1∕x)+3ˆ(1∕x))∕2]ˆx
= lim ln[(2ˆ(1∕x)+3ˆ(1∕x))∕2]/ (1/x)
= lim (ln2 2ˆ(1∕x)+ln3 3ˆ(1∕x))(-1/x^2)/2/[(2ˆ(1∕x)+3ˆ(1∕x))∕2] /(-1/x^2) ---- 罗比达法则
= lim ((ln2 2ˆ(1∕x)+ln3 3ˆ(1∕x))/2)/[(2ˆ(1∕x)+3ˆ(1∕x))∕2]
= (ln2 + ln3)/2
所以 lim(x→无穷)[(2ˆ(1∕x)+3ˆ(1∕x))∕2]ˆx = e^((ln2 + ln3)/2 )
= 根6