Final answer:
To find the limit of the expression as x approaches infinity, simplify the expression by dividing every term by the highest power of x and evaluate the limit.
Step-by-step explanation:
To find the limit as x approaches infinity of the expression √(4x^6-2x^3+1) - 2x^3, we can use the properties of limits. We can simplify the expression by dividing every term by the highest power of x, which is x^6. This gives us:
= √(4 - 2/x^3 + 1/x^6) - 2/x^3
As x approaches infinity, the terms with negative powers of x approach zero, leaving us with:
= √(4 - 0 + 0) - 0
= √4 - 0
= 2
Therefore, the limit of the expression as x approaches infinity is 2.