Questions: Determine the following limit or state that the limit does not exist. lim n → ∞ 4n = □

Transcript text: Determine the following limit or state that the limit does not exist. $\lim _{n \rightarrow \infty} 4 n=$ $\square$

Solution

Solution Steps

To determine the limit of the expression $ \lim_{n \rightarrow \infty} 4n $, we observe that as $ n $ approaches infinity, the term $ 4n $ will also approach infinity. Therefore, the limit does not exist because it diverges to infinity.

Step 1: Analyze the Limit

We need to evaluate the limit $ \lim_{n \rightarrow \infty} 4n $. As $ n $ approaches infinity, the expression $ 4n $ increases without bound.

Step 2: Determine the Behavior of the Expression

Since $ 4n $ grows indefinitely as $ n $ increases, we conclude that the limit diverges to infinity. Therefore, we state that the limit does not exist in the conventional sense.