Question

use the squeeze theorem to show that

lim x^4*cos(2/x) = 0
x->0

Answer 1

0<x^4*c0s(2/x)<x^4
apply lim x->0 u get the limit converges to 0

Answer 2

right, apply the limit to the right side (namely lim(x^4) as x-->4) and you get 0, so what's left in the middle must be both greater than or equal to and less than or equal to 0. so it must be zero, brilliant!