SOLUTION: find : limit (| sin (x) - 1|)/(sin (x) - 1) as x \[LongRightArrow] (pi)/2

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Question 1209179: find : limit (| sin (x) - 1|)/(sin (x) - 1) as x \[LongRightArrow] (pi)/2
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Note that since -1<=sin(x)<=1 for all x, -2<=sin(x)-1<=0 for all x, so |sin(x)-1|/(sin(x)-1)=(1-sin(x))/(sin(x)-1)=-1 for all x where sin(x) is not 1. This means that the limit at x=pi/2 is -1, since all the x-values close to it are always -1.