求该极限的求法如图 次方极限该怎么处理?
1个回答

y = (cosx)^(1/x^2)

lny = (1/x^2) ln cosx = lncosx / x^2 用洛必达法则:

lim(x->0) lny = lim(x->0) (-sinx/cosx) / 2x 再用一次洛必达法则

lim(x->0) -0.5 tanx/x = lim(x->0) 0.5 sec^2 x

= 0.5

即:lny = 1/2

lim(x->0) y = lim(x->0) (cosx)^(1/x^2)

= √e