How do you find the limit of #(xcosx)/sinx# as x approaches 2?

1 Answer
Sep 14, 2016

In finding limits always try substitution first.

Explanation:

#2# is close to #(2pi)/3# so #cos 2# is close to #cos((2pi)/3) = -1/2# and #sin2 ~~ sin((2pi)/3) = sqrt3/2#

We conclude that #cos 2 != 0# and #sin 2 != 0#.

Theerfore, we do not get an indeterminate form when we substitute.

#lim_(xrarr2) (xcosx)/sinx = (2cos2)/sin2# #" "# Which may also be written #2cot2#