Limit of \( \displaystyle \frac{x^{3} - 8}{x - 2} \) as \( x \to 2 \)

Problem 1.55 · easy

1. \[ \lim_{x \to 2^+}\left(\frac{x^{3} - 8}{x - 2}\right) \]
   limitStart with the limit of the function as x approaches 2 from the right.✓ Proved
2. \[ = \lim_{x \to 2^+}\left(x^{2} + 2 x + 4\right) \]
   factor cancelFactor the difference of cubes in the numerator. Cancel the common factor (x - 2) from the numerator and denominator.✓ Proved
3. \[ = 12 \]
   limitEvaluate the remaining polynomial at x = 2.✓ Proved