Calculate the limit LIM (below Lim is x → 2) x ^ 2-4 / x ^ 2-6x + 8

Calculate the limit LIM (below Lim is x → 2) x ^ 2-4 / x ^ 2-6x + 8

LIM (x → 2 under LIM) x ^ 2-4 / x ^ 2-6x + 8 = LIM (x → 2 under LIM) (X-2) (x + 2) / X-2) (x-4)
LIM (below Lim is x → 2) (x + 2) / (x-4) = - 2

Let LIM (x → 1) sin (x ∨ 2-1) / X ∨ 3-A = 2 / 3

When x approaches to 1, sin (x ^ 2-1) above can be replaced by (x ^ 2-1) with the same denominator, because the result is 2 / 3. At this time, if x is 1 in the numerator, the result is 0, and the result is 2 / 3. Therefore, we can see that the numerator and denominator can divide each other and reduce (x-1) in the numerator, which excludes the numerator

What is Lim sin (x-1) / x ^ 2-1 when x → 1
X ^ 2 is the second power of X,

When x → 1, Lim [sin (x-1) / (x-1)] = Lim [sin (x-1) / (x-1)] · 1 / (x + 1) = Lim [sin (x-1) / (x-1)] · Lim1 / (x + 1) = 1.1 / (1 + 1) = 1 / 2