Question

find limx→π+ csc(2x)
is it positive or a negative limit?

Answer 1

\[\lim_{x \rightarrow \pi} \csc(2x)\]
written like this ?

Answer 2

yup

Answer 3

now you know the relationship between csc and sin ?

Answer 4

yeah reciprocals right?

Answer 5

it's called inverse actually : csc(x)=1/sin(x)

Answer 6

my bad

Answer 7

now csc(2x)=1/sin(2x)

Answer 8

now sin(2x)=sin(x+x)
which is....

Answer 9

sin(a+b)=...

Answer 10

continue

Answer 11

yeah I'm lost

Answer 12

sin(a+b)=?

Answer 13

you have a formula for this

Answer 14

sin(a+b)=sin(a)cos(b)+sin(b)cos(a)

Answer 15

now sin(x+x)=...

Answer 16

sin(2x)

Answer 17

use the formula mate

Answer 18

replace x with a and x with b and add that sum

Answer 19

sin(a+b) ??

Answer 20

what?

Answer 21

sin(2x)=2sinxcosx

Answer 22

now

Answer 23

your limit can be written in this form
\[\lim_{x \rightarrow \pi}\frac{ 1 }{ 2\sin x \cos x }\]

Answer 24

now replace x with pi and do the math...

Answer 25

.027 ?

Answer 26

thank you i got it