Question

求解几道高数极限，谢谢(*°∀°)=3！

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Answer 1

(10)

x->0
e^(3x)~ 1+3x
e^(3x) -5x ~ 1-2x
---------
lim(x->+∞) ( e^(3x)-5x)^(1/x)
=lim(x->+∞) ( 1-2x)^(1/x)
=e^(-2)
(11)
x->0
sinx ~ x
cosx ~ 1
2sinx +cosx ~ 1+2x
---------

lim(x->+∞) (2sinx+cosx)^(1/x)
=lim(x->+∞) ( 1+2x)^(1/x)
=e^2
(12)
L = lim(x->0+) (1/x)^tanx
lnL
=lim(x->0+) ln(1/x)/cotx (∞/∞)
=lim(x->0+) (-1/x)/(-cotx.cscx)
=lim(x->0+) 1/cscx
=lim(x->0+) sinx
=0
L = e^0 =1