Question

Evaluate the following
Lim (xcotx)
x->00

Answer 1

1

Explanation:

Evaluate the following

Lim (xcotx)

x->0

Note that cotx = cosx/sinx

The expression becomes

Lim (xcotx) = Lim (xcosx/sinx)

x->0 x->0

= 0cos0/sin0

= 0/0 )(ind)

Apply l'hospital rule

= Lim d/dx(xcosx/sinx)

x->0

= lim (-xsinx + cosx)/cosx

x->0

= -0sin0+cos0/cos0

= 0+1/1

= 1/1

= 1

Hence the limit of xcotx as x tends to zero is 1