Find the following limit. \[ \lim _{x \rightarrow 0}\left(x^{4} \sin \frac{1}{x}+3\right) \] If the limit does not exist, click on "Does Not Exist."

Step 1 ：The limit of a sum is the sum of the limits, provided that the limits exist. So, we can break this limit into two parts: \(\lim _{x \rightarrow 0} x^{4} \sin \frac{1}{x}\) and \(\lim _{x \rightarrow 0} 3\).

Step 2 ：The second limit is easy to compute, it's just 3.

Step 3 ：The first limit is a bit more complicated. We can see that as x approaches 0, the term \(x^{4}\) approaches 0. However, the term \(\sin \frac{1}{x}\) oscillates between -1 and 1. But since \(x^{4}\) is approaching 0 faster than \(\sin \frac{1}{x}\) is oscillating, the whole term should approach 0.

Step 4 ：Combining these two limits, we get the final limit as 3.

Step 5 ：Final Answer: The limit of the given function as \(x\) approaches 0 is \(\boxed{3}\).