Question

date: work for monday, october 6th, 2025 using algebraic manipulation 2. $lim_{x
ightarrow1}\frac{2x - 2}{x - 1}$ 4.

Explanation:

Step1: Factor the numerator

Factor out 2 from the numerator $2x - 2$ to get $2(x - 1)$. So the limit becomes $\lim_{x
ightarrow1}\frac{2(x - 1)}{x - 1}$.

Step2: Simplify the fraction

Cancel out the common factor $(x - 1)$ in the numerator and denominator. We get $\lim_{x
ightarrow1}2$.

Step3: Evaluate the limit

Since the function is now a constant function $y = 2$, as $x$ approaches 1, the value of the function is 2.

Answer:

2