Question

Can somebody help me ASAP. I attached a picture.

Answer 1

½

Explanation:

cot(2x) = 1/(tan(2x))

csc(x) = 1/(sin(x))

cot(2x)/csc(x) = sin(x)/tan(2x)

As x --> 0 this fraction is 0/0 which is an indeterminate form.

Using L'Hopital

Derivatives:

sin(x) ---> cos(x)

tan(2x) ---> 2sec²(2x)

cos(x)/(2sec²(2x))

= ½ as x --> 0