Final answer:
To evaluate the limit limₓ → ₂ (x³ + 6x³ + 7), combine like terms, factor out a common factor of 7, and substitute x = 2 into the expression to get 63.
Step-by-step explanation:
To evaluate the limit limx → 2(x³ + 6x³ + 7), we can simplify the expression first by combining like terms. This gives us 7x³ + 7. Next, we can factor out a common factor of 7 to get 7(x³ + 1). Finally, we substitute x = 2 into the expression, giving us 7(2³ + 1) = 7(8 + 1) = 7(9) = 63.