lim sinx

as x approaches pie/r

That would just be the sine of pi/r.

The limit value would depend upon what r is. There are no singularities, such as 0/0. Are you sure you copied the problem correctly?

That's how the question reads. these are the choices for answers

A) -(2^1/2)/2
B) (2^1/2)/2
C) (2^-1/2)/4
D) DOES NOT EXIST
E) -(2^(-1/2))/4

I'm assuming since there is no value for R then the answer does not exist?

The question choices make no sense. I suspect a typo error regarding the "r" term, perhaps a teacher error. A limit does exist, and it is sin pi/r

To evaluate the limit of sin(x) as x approaches π/3, we can directly substitute the value of π/3 into the expression.

lim sin(x) = sin(π/3)

The sine of π/3 can be calculated using the unit circle or a calculator. The value of sin(π/3) is √3/2.

Therefore, the limit of sin(x) as x approaches π/3 is √3/2.