Lim 3x/tan3x x →0 How to solve it ? I think the answer will be 1 or -1 who can solve it ?

1 Answer

The limit is 11.

Explanation:

Lim_(x -> 0)(3x)/(tan3x)

=Lim_(x -> 0)(3x)/((sin3x)/(cos3x))

=Lim_(x -> 0)(3xcos3x)/(sin3x)

=Lim_(x -> 0)(3x)/(sin3x).cos3x

=Lim_(x -> 0)color(red)((3x)/(sin3x)).cos3x

=Lim_(x -> 0)cos3x

=Lim_(x -> 0)cos(3*0)

= Cos(0) = 1



Remember that:

Lim_(x -> 0)color(red)((3x)/(sin3x))=1

and

Lim_(x -> 0)color(red)((sin3x)/(3x))=1