Limit of \( \displaystyle \frac{4 x^{2} - 4}{2 x - 2} \) as \( x \to 1 \)

Problem 1.62 · medium

1. \[ \lim_{x \to 1^+}\left(\frac{4 x^{2} - 4}{2 x - 2}\right) \]
   limit algebraStart with the limit of the original function. Factor out the constant 4 from the numerator.✓ Proved
2. \[ = \lim_{x \to 1^+}\left(\frac{\left(x + 1\right) \left(4 x - 4\right)}{2 x - 2}\right) \]
   factor rewriteFactor the difference of squares in the numerator. Factor the denominator.✓ Proved
3. \[ = \lim_{x \to 1^+}\left(2 x + 2\right) \]
   cancel simplifyCancel the common factor (x - 1). Simplify the fraction.✓ Proved
4. \[ = 4 \]
   limitEvaluate the limit by substituting x = 1.✓ Proved