Question

Evaluate this ------→

lim x → 1 (x²-2x+1)/x²-1​

Answer 1

Step-by-step explanation:

lim(x -> 1) (x² - 2x + 1) /(x² - 1)

Substituting x = 1

(1² - 2*1 + 1)/(1² - 1) = 0/0

Use LHospital Rule

Differentiating the numerator and denominator wrt x,

Numerator becomes 2x - 2

Denominator becomes 2x

Now,

lim( x -> 1) (2x - 2)/(2x)

Substituting x = 1

(2*1 - 2)/(2*1) = (2 - 2)/2 =0/2= 0

Answer 2

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