Evaluate \( \lim _{x \rightarrow \infty} \frac{x+17}{3-4 x} \). If the corresponding limit is infinity, then insert INF in the blank. If the corresponding limit is negative infinity, then insert -INF in the blank. If the corresponding limit does not exist, then insert DNE in the blank. Otherwise, write the number as an integer or a reduced fraction.

To evaluate the limit: \[ \lim_{x \rightarrow \infty} \frac{x + 17}{3 - 4x} \] Let's analyze the behavior of the function as \( x \) approaches infinity. 1. **Leading Terms Dominance**: - In the numerator, the leading term is \( x \). - In the denominator, the leading term is \( -4x \). 2. **Simplifying the Expression**: \[ \frac{x + 17}{3 - 4x} \approx \frac{x}{-4x} = -\frac{1}{4} \] 3. **Conclusion**: As \( x \) becomes very large, the lower-order terms (17 in the numerator and 3 in the denominator) become negligible compared to the leading terms. Therefore, the limit is determined by the ratio of the leading coefficients. \[ \lim_{x \rightarrow \infty} \frac{x + 17}{3 - 4x} = -\frac{1}{4} \] **Answer:** \(-\frac{1}{4}\)