`lim_(xrarr0)(sin(x)/(4))/(x)`

Answer

To solve the limit \( \lim_{x \to 0} \frac{\sin(x)/4}{x} \), we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Limit:**
We can rewrite the limit as:
\[ \lim_{x \to 0} \frac{\sin(x)}{4x} \]

2. **Factor Out the Constant:**
Since \( \frac{1}{4} \) is a constant, we can factor it out of the limit:
\[ \lim_{x \to 0} \frac{\sin(x)}{4x} = \frac{1}{4} \lim_{x \to 0} \frac{\sin(x)}{x} \]

3. **Use the Standard Limit Result:**
We know from standard calculus that:
\[ \lim_{x \to 0} \frac{\sin(x)}{x} = 1 \]
Therefore, we can substitute this result into our limit:
\[ \frac{1}{4} \lim_{x \to 0} \frac{\sin(x)}{x} = \frac{1}{4} \cdot 1 \]

4. **Calculate the Final Result:**
Thus, we have:
\[ \frac{1}{4} \cdot 1 = \frac{1}{4} \]

### Final Answer:
The value of the limit is:
\[ \frac{1}{4} \]