Question

evaluate the limit.
lim (7t - 9)
t→∞
simplify any fractions in your answer.

Explanation:

Step1: Analyze the term \(7t\)

As \(t\to\infty\), the term \(7t\) will approach \(\infty\) since \(7>0\) and \(t\) is getting larger and larger. Mathematically, \(\lim_{t\to\infty}7t=\infty\).

Step2: Analyze the constant term \(- 9\)

The limit of a constant \(c\) as \(t\to a\) (where \(a\) can be \(\infty\)) is just the constant itself. So, \(\lim_{t\to\infty}(-9)=-9\).

Step3: Use the limit property \(\lim_{t\to a}(f(t)+g(t))=\lim_{t\to a}f(t)+\lim_{t\to a}g(t)\)

We have \(\lim_{t\to\infty}(7t - 9)=\lim_{t\to\infty}7t+\lim_{t\to\infty}(-9)\). Substituting the values from Step 1 and Step 2, we get \(\infty+( - 9)\).

Answer:

\(\infty\)