Evaluate the following limits `lim_(x to 4)(4x+3)/(x-2)`

Answer

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

### Step 1: Substitute the value of \( x \)
We start by substituting \( x = 4 \) directly into the expression:

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

### Step 2: Calculate the numerator
Now, calculate the numerator:

\[ 4(4) + 3 = 16 + 3 = 19 \]

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

\[ 4 - 2 = 2 \]

### Step 4: Combine the results
Now, substitute the results back into the limit expression:

\[ \frac{19}{2} \]

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

\[ \lim_{x \to 4} \frac{4x + 3}{x - 2} = \frac{19}{2} \]

### Final Answer
\[ \frac{19}{2} \]

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