lim(x→0)[(tanx)^2-x^2]/x^4

Question

lim(x→0)[(tanx)^2-x^2]/x^4

Answer 1

=lim(x→0)(tanx-x)/x^3·lim(x→0)(tanx+x)/x
=lim(x→0)[(secx)^2-1]/(3x^2)·lim(x→0)(tanx/x+1)
=lim(x→0)(tanx)^2/(3x^2)·2
=1/3·2
=2/3