求极限,快刀手来啊!当x——>0时,{x^2-（tanx）^2}/x^4

Question

求极限,快刀手来啊!当x——>0时,{x^2-（tan x）^2}/x^4

Answer 1

lim(x——>0){x^2-（tan x）^2}/x^4
=lim(x->0)(x-tanx)(x+tanx)/x^4
=lim(x->0)(x-tanx)/x³*(x+tanx)/x
=2lim(x->0)(x-tanx)/x³
=2lim(x->0)(1-sec²x)/3x²
=2lim(x->0)(-tan²x)/3x²
=2lim(x->0)(-x²)/3x²
=-2/3