Question

How do you find the limit of `(sin(-2x)) / x` as x approaches 0?

Answer 1

The limit is `-2`

Explanation:

Set `u=-2x=>x=-1/2*u` so now we have that

#lim_(x->0)[sin(-2x)/x]=lim_(u->0)[sinu/(-1/2*u)]= -2*lim_(u->0)[sinu/u]=-2#

The limit is `-2`

Note : It is known that `lim_(x->0)sinx/x=1`