Limit of \( \displaystyle 6 x + \left(2 x - 1\right)^{2} - 4 \) as \( x \to \frac{3}{2} \)

Problem 1.226 · medium

1. \[ \lim_{x \to \frac{3}{2}^+}\left(6 x + \left(2 x - 1\right)^{2} - 4\right) \]
   limit algebraEvaluate the limit of the function at x = 3/2. Rearrange the terms.✓ Proved
2. \[ = \lim_{x \to \frac{3}{2}^+}\left(4 x^{2} + 2 x - 3\right) \]
   simplify simplifyExpand the squared binomial. Combine like terms.✓ Proved
3. \[ = 9 \]
   limit simplify simplifySubstitute the value x = 3/2 into the expression. Evaluate the exponent. Final calculation.✓ Proved