Show that the limit for [x^2cos(1/x)]=0 as x approaches 0.

Question

How would I solve this algebraically?

Answer 1

Hmmm.

lim(x^2 cos1/x)=limx^2 * lim cos1/x

but cosine is limited to between 1 and -1
but lim x^2 rapidly approaches zero, so since zero times any finite number is zero...
limit is zero