# How do you find #lim root3(t^3+1)-t# as #t->oo#?

Use the difference of cubes identity:

So:

So:

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To find the limit of √(3(t^3+1) - t) as t approaches infinity, we can simplify the expression and apply the limit rules.

First, let's simplify the expression inside the square root: √(3(t^3+1) - t) = √(3t^3 + 3 - t)

Next, as t approaches infinity, we can ignore the constant term "3" and "-t" since they become insignificant compared to the dominant term "3t^3".

Therefore, the expression simplifies to: √(3t^3)

Now, we can take the limit as t approaches infinity: lim √(3t^3) = √(lim 3t^3)

Since the limit of 3t^3 as t approaches infinity is infinity, the final answer is: lim √(3(t^3+1) - t) as t approaches infinity is also infinity.

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