No, cos(∞) is undefined; the limit does not exist.
Here's why:
The cosine function, cos(x), oscillates between -1 and 1 as x increases. As x approaches infinity, cos(x) continues to oscillate indefinitely and does not approach a specific value.
Think of it like this: Imagine walking around a circle. As you keep walking, your x-coordinate (which is related to the cosine value) keeps changing between -1 and 1. Even if you walk "forever" (approaching infinity), your x-coordinate never settles down to a single, defined value.
Since the cosine function's output doesn't converge to a particular value as its input approaches infinity, we say that the limit of cos(x) as x approaches infinity does not exist. Consequently, cos(∞) is undefined.
