find limit of .......lim (x->0)....cot(x) - csc(x)?

Question

please help i dont know how to do this

Answer 1

[x→0]lim cot x - csc x
[x→0]lim cos x/sin x - 1/sin x
[x→0]lim (cos x - 1)/sin x

Using L'hopital's rule:

[x→0]lim -sin x/cos x
0/1
0

Answer 2

lim x->0 cos(x)/x DNE lim (x-)->0 cos(x)/x = -(cos(0)/0) = -a million/0 = -? lim (x+)->0 cos(x)/x = (cos(0)/0) = a million/0 = ? The shrink itself does not exist. additionally, in case you advise lim x->0 (cos(x/x)) then it would incredibly be cos(a million). the graph of cos(x/x) is a right this moment away horizontal line that has a hollow at x=0.