Question

Find the limit. Use l'Hospital's Rule

Answer 1

\[\lim_{x \rightarrow 0}(cotx-\frac{ 1 }{ x})\]

Answer 2

The limit does not exist.

Answer 3

how did you come up with this conclusion?

Answer 4

first use an identity to change cotx int fraction
then combine the fractions
then you can start using l'hospitals rule

Answer 5

is there any simpler way without using that rule?

Answer 6

using the rule is much easier way to do it

Answer 7

can i just plug in 0 for x?

Answer 8

yeah, but that would give u indeterminate solution, which is not what you should be looking for

Answer 9

oh ok, so to change cotx into a fraction do i use 1/cosx

Answer 10

no never mind is 1/tanx

Answer 11

yeah, but tan would always give you zero, so it's better to use cos/sin

Answer 12

ok if i combine the 2 fractions would it be cos/sinx^2