Evaluate : `lim_(x to 3)[x(x+1)]`.

Answer

To evaluate the limit \( \lim_{x \to 3} [x(x+1)] \), we can follow these steps:

### Step 1: Substitute the value of \( x \)
We start by substituting \( x = 3 \) directly into the expression \( x(x+1) \).

\[ x(x+1) = 3(3+1) \]

### Step 2: Simplify the expression
Now we simplify the expression inside the limit:

\[ 3(3+1) = 3 \times 4 \]

### Step 3: Calculate the product
Now we calculate the product:

\[ 3 \times 4 = 12 \]

### Conclusion
Thus, the limit is:

\[ \lim_{x \to 3} [x(x+1)] = 12 \]

### Final Answer
The final answer is \( 12 \).

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