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Chapter 7: Problem 1

Evaluate \(\lim _{n \rightarrow \infty} \frac{3 n+5}{2 n-7}\).

Short Answer

Expert verified
The limit of the function \(\frac{3n+5}{2n-7}\) as \(n\) approaches infinity is \(\frac{3}{2}\).

Step by step solution

01

Identify the leading coefficients

In the given function, the leading term in the numerator is \(3n\), and the leading term in the denominator is \(2n\). The leading coefficients are 3 and 2, respectively.
02

Calculate the ratio of the leading coefficients

As the degrees of the numerator and the denominator are the same, the limit is the ratio of the leading coefficients, which is: \[\frac{3}{2}\]
03

Write the final answer

So, the limit of the function as \(n\) approaches infinity is: \[\lim_{n \rightarrow \infty} \frac{3n+5}{2n-7} = \frac{3}{2}\]

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