Can you please show stepsplease Determine the limit of the t

Can you please show steps..please

Determine the limit of the trigonometric function (if it exists). (If an answer does not exist, enter DNE.) lim cos (2 ) tan (2 ) /

Solution

lim       cos(2)*tan(2) /

->0

we know that   lim     tan x / x = 1

                         x->0

so we multiply an divide the given expression by 2

lim     2*cos(2)*(tan(2) / 2)

->0

also lim cos x = 1

       x->0

as ->0 , 2 also goes to zero.

there fore     lim cos 2 = 1    and lim tan 2 / 2   = 1

                    ->0                            ->0

lim       cos(2)*tan(2) /    = 2

    ->0