The lim(X→1) (X^2-1)/(X-1) is

In order to find this limit, we need to get rid of the conflicting x - 1 factor in the denominator that is causing division by zero. To do this, note that the numerator factors as a difference of squares to:
x^2 - 1 = (x + 1)(x - 1).

So, we have:
lim (x-->1) (x^2 - 1)/(x - 1) = lim (x-->1) (x + 1)(x - 1)/(x - 1)
= lim (x-->1) (x + 1), by canceling the conflicting x - 1 factor
= 1 + 1, by evaluating the result at x = 1
= 2.

Note that the cancellation of the x - 1 factor made a new expression that is defined at x = 1, which allowed us to evaluate the limit by substituting x = 1 into that expression.

I hope this helps!

Use L'Hopital's Rule and find the first derivative of both the numerator and denominator.

= lim(X→1) 2x / 1 = 2

answer is 2

limit x---->1 (x^2-1)/( x-1)
= limx---> 1(x-1)(x+1)/(x-1)
= limx---> 1( x+1)
= 2 answer

lim(x->1) (x+1)(x-1)/(x-1)
=2 Ans.