SOLUTION: Calculus 1 limits worksheet 4 evaluating limits by ... - Free Printable

Final Answer:
8

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Explanation:
Let’s solve this step by step.

We are given:

lim as x → 0 of [ (4 + x)² - 16 ] / x

Step 1: Expand the top part — (4 + x)²
(4 + x)² = 4² + 2·4·x + x² = 16 + 8x + x²

So now the expression becomes:
[16 + 8x + x² - 16] / x

Step 2: Simplify the top
16 - 16 cancels out → leaves us with 8x + x²

Now we have:
(8x + x²) / x

Step 3: Factor x from the top
= x(8 + x) / x

Step 4: Cancel x on top and bottom (as long as x ≠ 0, which is fine because we’re taking the limit as x approaches 0, not actually plugging in 0)

Left with: 8 + x

Step 5: Now plug in x = 0
8 + 0 = 8

✔ So the answer is 8.