Question

Explain this limit please.

Answer 1

Why is \[\lim_{x \rightarrow 0} \frac{ x+2 }{ cotx } = 0 \] and not \[\lim_{x \rightarrow 0} \frac{ x+2 }{ cotx } = dne?\]

Answer 2

because \[\lim_{x\to 0}\cot(x)=\infty\]

Answer 3

well actually plus or minus infinity, but no matter
the numerator goes to 2 and the denominator goes to one or the other

Answer 4

also,
\[\lim_{x->0} \frac{ x+3 }{ cotx } = \lim_{x->0} (x+3)tanx\]

Answer 5

yeah, that too

Answer 6

@Euler271 \to

Answer 7

think zarkon showed me that one

Answer 8

actually I think limit as x approaches 0 to cotx is actually dne, since both directions are different.

Answer 9

that is true.

the limit does not exist since its -inf from left and +inf from right

Answer 10

however, 1/inf = 1/(-inf) = 0