Evaluate : `lim_(x to 2)(4x+3)/(x+2)`.

Answer

To evaluate the limit \( \lim_{x \to 2} \frac{4x + 3}{x + 2} \), we will follow these steps:

### Step 1: Substitute \( x = 2 \) into the expression
We start by substituting \( x \) with 2 in the expression:

\[ \frac{4(2) + 3}{2 + 2} \]

### Step 2: Calculate the numerator
Now, let's calculate the numerator:

\[ 4(2) + 3 = 8 + 3 = 11 \]

### Step 3: Calculate the denominator
Next, we calculate the denominator:

\[ 2 + 2 = 4 \]

### Step 4: Form the final expression
Now we can form the final expression by combining the results from the numerator and denominator:

\[ \frac{11}{4} \]

### Step 5: State the limit
Thus, the limit is:

\[ \lim_{x \to 2} \frac{4x + 3}{x + 2} = \frac{11}{4} \]

### Final Answer
The final answer is:

\[ \frac{11}{4} \]

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