Points] DETAILS MY NOTES SCALCET9 2.XP.6.005. Find the limit. (If the limit is infinite, enter ' \( \infty \) ' or '- \( -\infty \) ', as appropriate. If the limit does not otherwise exist, enter ONI \( \lim _{x \rightarrow \infty} \frac{5 x-7}{2 x+3} \)

To find the limit as \( x \) approaches infinity for the expression \( \frac{5x - 7}{2x + 3} \), we can divide every term in the numerator and the denominator by \( x \): \[ \lim_{x \rightarrow \infty} \frac{5 - \frac{7}{x}}{2 + \frac{3}{x}} \] As \( x \) approaches infinity, \( \frac{7}{x} \) and \( \frac{3}{x} \) both approach 0. Thus, the limit simplifies to: \[ \frac{5 - 0}{2 + 0} = \frac{5}{2} \] So the limit is \( \frac{5}{2} \). However, once we break it down, we can recall that understanding the behavior of functions as they grow larger often involves recognizing dominant terms. The leading coefficients in both the numerator and denominator guide the limit, allowing you to reach the conclusion swiftly!