Question

limit as x goes to 0:
(3x)/(cot(4x))

Answer 1

change cot right?

Answer 2

You can.
lim x->0 (3x)(sin(4x))/(cos(4x)
Which gives you zero.

Answer 3

why is that though?

Answer 4

Because 3(0)sin(0)/cos(0)=0/1 or just 0.

Answer 5

oh, I see you substitute x in this case because it can not be factored or broken down any further

Answer 6

thanks!

Answer 7

\[{3x \over cot(4x)} = {3x \over {1 \over tan(4x)}} = 3x (tan(4x)) = {3x(sin( 4x))\over cos(4x)}\]

Answer 8

And then yeah the limit of a quotient is the quotient of the limits. cos(4x) goes to 1, 3x goes to 0, sin(4x) goes to 0. So you have 0 over 1 which is 0.