Question

how is the limit of x^2/(1-cos^2(x)) as x goes to 0 is 1. I know how to show this using l'hopital rule. But can you show this using the rule that limit of (1-cosx)/x=1 as x goes to 0 and limit of sinx/x=1 as x goes to 0

Answer 1

1 -cos^2 x=sin^2x

lim (x/sinx)(x/sinx)=lim x/sinx lim x/sinx=1

remember if lim a/b = 1, then lim b/a has to equal 1.