We have to find the value of (x^2+2x-3)/|x-1| as x approaches from the left.
As x approaches from the left x - 1 is always negative, so we have |x - 1| = (1 - x)
lim x--> 1 [ (x^2+2x-3)/(1 - x)]
lim x--> 1 [ (x^2+3x - x-3)/(1...
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We have to find the value of (x^2+2x-3)/|x-1| as x approaches from the left.
As x approaches from the left x - 1 is always negative, so we have |x - 1| = (1 - x)
lim x--> 1 [ (x^2+2x-3)/(1 - x)]
lim x--> 1 [ (x^2+3x - x-3)/(1 - x)]
lim x--> 1 [ (x(x + 3) - 1(x + 3)/(1 - x)]
lim x--> 1 [ (x - 1)(x + 3)/(1 - x)]
lim x--> 1 [ -(x + 3)]
substitute x = 1
=> - 4
The required value of the limit is -4