SOLUTION: please help
f(x)=(x²-4)/|x-2| find each limit (if possible)
a) lim as x→2 from left f(x)
b)lim as x→2 from right f(x)
c)lim as x→2 f(x)
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f(x)=(x²-4)/|x-2| find each limit (if possible)
a) lim as x→2 from left f(x)
b)lim as x→2 from right f(x)
c)lim as x→2 f(x)
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Question 1090027: please help
f(x)=(x²-4)/|x-2| find each limit (if possible)
a) lim as x→2 from left f(x)
b)lim as x→2 from right f(x)
c)lim as x→2 f(x) Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website! The function is
or
The function is clearly undefined at x=2, since the denominator will be 0. The limit as x approaches 2 will exist if and only if the limits as you approach 2 both from the left and from the right are the same.
For values of x less than 2, |x-2| = -(x-2), so
so the function is equivalent to -(x+2), or
f(x) = -x-2
So as you approach 2 from the left, the function value approaches
-2-2 = -4
For values of x greater than 2, |x-2| = (x-2), so
so the function is equivalent to
f(x) = 1(x+2) = x+2
So as you approach 2 from the left, the function value approaches
2+2 = 4
So the answers are
a) the limit as x approaches 2 from the left is -4
b) the limit as x approaches 2 from the right is 4
c) the limit as x approaches 2 does not exist, because the limits from
the left and right are not the same
