RaySix

Post

at November 4th 2023, 5:26:15 pm.

Question: Find the limit of the following algebraic function algebraically:

\lim_{x \to 2} \frac{x^2 - 4x + 4}{x - 2}

Answer:

To find the limit of the given function as x approaches 2, we can first simplify the function by factoring the numerator:

\lim_{x \to 2} \frac{(x - 2)(x - 2)}{x - 2}

Here, we can see that the term $(x - 2)$ exists in both the numerator and denominator. We can cancel out this term:

\lim_{x \to 2} (x - 2)

Now, as x approaches 2, we can simply plug in 2 for x:

\lim_{x \to 2} (x - 2) = 2 - 2 = 0

Hence, the limit of the given function as x approaches 2 is 0.

Thus, the final answer is:

\boxed{\lim_{x \to 2} \frac{x^2 - 4x + 4}{x - 2} = 0}