求助为什么有的3分之1，有的9分之2

x->0
(3+2tanx)^x
=3^x.[1+(2/3)tanx]^x
~3^x.[1+(2/3)x]^x
~3^x.e^[(2/3)x^2]
(3+2tanx)^x-3^x
~3^x.e^[(2/3)x^2] -3^x
=3^x.[e^[(2/3)x^2] -1]
~ [e^[(2/3)x^2] -1]
~(2/3)x^2
lim(x->0) [ (3+2tanx)^x-3^x ]/ [3(sinx)^2 +x^3.cos(1/x)]
=lim(x->0) [ (3+2tanx)^x-3^x ]/ [3x^2 +x^3.cos(1/x)]
=lim(x->0) (2/3)x^2/ [3x^2 +x^3.cos(1/x)]
=lim(x->0) (2/3)/ [3 +x.cos(1/x)]
=(2/3)/(3+0)
=2/9