Find the limit as x approaches 0 (x^2(1-cot^2(x)))?

Question

experimentx · Answer

experimentx · Answer

lim x-> 0 x^2(1-cot^2(x))
= lim x-> 0 x^2-x^2 cot^2(x)
= lim x-> 0 0 - x^2/sin^2 x * cox^2 x
= lim x-> 0 -cos^2 x/ (sin x/x)^2
= -1

anonymous · Answer

I dont think I follow this, did you distribute the x^2 out in the second line?

experimentx · Answer

x^2(1-cot^2(x))  = x^2  - x^2 cot^2 x (distributive property)

anonymous · Answer

okay, I got that now. Could you explain what you did after that?

experimentx · Answer

lim x->0 x^2 - x^2 cot^2 x = (lim x->0 x^2) - (lim x->0 cot^2 x)

anonymous · Answer

okay so x^2/sin^2x would equal 1, if im following what you did correctly

experimentx · Answer

yeah .. and that cos^2 x = 1 too

anonymous · Answer

Oh okay, thank you I understand this now!!