Question

帮忙解解🙏

Answer 1

x->0
cosx ~ 1- (1/2)x^2
(cosx)^2 ~[1- (1/2)x^2]^2
~ 1 - x^2
x^2.(cosx)^2 ~ x^2 - x^4

sinx ~ x - (1/6)x^3
(sinx)^2 ~ [x - (1/6)x^3]^2
~ x^2 - (1/3)x^4
(sinx)^2 -x^2.(cosx)^2 ~ (2/3)x^4

e^(2x) -1 ~ 2x
ln(1+(tanx)^2) ~ x^2
x(e^(2x)-1).ln(1+(tanx)^2) ~ 2x^4

lim(x->0) [(sinx)^2 -x^2.(cosx)^2]/[x(e^(2x)-1).ln(1+(tanx)^2)]
=lim(x->0) (2/3)x^4/(2x^4)
=1/3
ans:B