how do i find the limit of this?

Question

(This symbol:-> is an arrow)

lim of x-> 0 sin^2x/x

can someone please explain?

Answer 1

When an expression involves a division, and the denominator becomes indefinite or zero at the limit, l'Hôpital's rule can be used.

To apply l'Hôpital's rule, take the derivative of the numerator and the denominator, and try to evaluate the expression at the required limit. If the denominator is still indefinite, repeat the procedure.

In the particular case,

Lim x→0 sin²(x)/x
=Lim x→0 2sin(x)cos(x)/1
=2sin(0)cos(0)/1
=2*0*1/1
=0