Problem
5. [-/1 Points] DETAILS SCALC9 3.4.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the limit using the appropriate properties of limits. (If the limit is infinite, enter ' $\infty$ ' or '- $\infty$ ', as appropriate. If the limit does not otherwise exist, enter DNE.) \[ \lim _{x \rightarrow \infty} \frac{6 x^{2}-5}{7 x^{2}+x-3} \] Need Help? Read It Watch it Master It Submit Answer
Solution
Step 1 ：The limit is a ratio of two polynomials of the same degree. In such cases, the limit as x approaches infinity is the ratio of the leading coefficients. In this case, the leading coefficients are 6 and 7. Therefore, the limit should be \(\frac{6}{7}\).
Step 2 ：Final Answer: \(\boxed{\frac{6}{7}}\)
