lim _(n arrow infty)(sqrt(n^2)+3 cdot 5 cdot n-5)

To find the limit of the given expression as approaches infinity, we can simplify the expression inside the square root.First, let's rewrite the expression inside the square root: This simplifies to: Next, we can factor out from the terms inside the square root: Now, we can take the square root of outside the square root: As approaches infinity, the terms and approach 0. Therefore, the expression simplifies to: So, the limit of the given expression as approaches infinity is .