i get the answer 0 ( not sure if it is right ) but how i get does not make sense to me.
lim SQRT of X / CSC X
x approaches PI
in place of PI i use 180 ( this is where i think im wrong but 3.141… doest make sense to use either.)
and csc = 1/sin x
so…
SQRT PI / 1/sin PI
from there
sqrt PI * sinPI / 1
sin 180 = 0
sqrt PI * 0 = 0
I think you’ve got the right answer.
Sin(X) approaches zero as X approaches Pi.
So CSC(X) approaches infiniti as X approaches Pi.
Anything divided by infiniti = 0.
so
Sqrt(anything divided by infiniti) = 0
Your algebra is correct, you could also arrive there by some analysis.
csc(x) as x -> pi becomes infinitely large.
You cannot directly compute sqrt(x), as x -> pi, since pi is irrational and has no square root.
BUT, since csc(x), x -> pi, becomes huge the closer and closer you get to pi, and since sqrt(x), x->pi, is roughly constant. You have a denominator that is increasingly increasing, and a “constant” numerator. Thus it must tend to 0.
Hope that helps with the reasoning.