Question 1028822
limit as x approaches pi of (sin(x-pi)) / (x-pi)
:
simplify the expression inside the limit
:
(sin(x-pi)) / (x-pi) = sin(x) / (pi-x)
:
limit as x approaches pi of sin(x) / (pi-x)
:
this intermediate result is of the form 0/0, apply l'Hopital's rule
:
limit as x approaches pi of sin(x) / (pi-x) = limit as x approaches pi of (d sin(x)/dx) / d (pi-x)/dx) =
:
limit as x approaches pi of cos(x) / -1 =
:
limit as x approaches pi of -cos(x)
:
substitute pi for x in the expression
:
**************************************************
limit as x approaches pi of -cos(x) = -cos(pi) = 1
**************************************************
: