**Understanding the Problem:**
We are given a function f(x) and we need to find the limit of f(x) as x tends to infinity. The function is defined as:
f(x) = [(x-1)(x-2)(x-3)...(x-2023)]^(1/2023) - x

**Expanding the Function:**
Let's first expand the function [(x-1)(x-2)(x-3)...(x-2023)]^(1/2023) using the binomial theorem:
[(x-1)(x-2)(x-3)...(x-2023)]^(1/2023) = (x^2023 - (1+2+3+...+2023)x^2022 + (terms with lower powers of x))

**Simplifying the Function:**
Now, let's simplify the function by keeping only the dominant terms as x tends to infinity.
As x tends to infinity, the lower powers of x become negligible compared to the highest power of x (x^2023). So, we can ignore the terms with lower powers of x.

Therefore, the simplified function becomes:
[(x-1)(x-2)(x-3)...(x-2023)]^(1/2023) ≈ x - (1+2+3+...+2023)

**Calculating the Sum of Natural Numbers:**
Now, let's calculate the sum of the first 2023 natural numbers:
Sum = 1 + 2 + 3 + ... + 2023 = (2023 * (2023 + 1)) / 2 = 2047476

**Final Simplified Function:**
Substituting the value of the sum in the simplified function, we get:
[(x-1)(x-2)(x-3)...(x-2023)]^(1/2023) ≈ x - 2047476 - x

Simplifying further, we get:
[(x-1)(x-2)(x-3)...(x-2023)]^(1/2023) ≈ -2047476

**Calculating the Limit:**
Finally, we take the limit of the simplified function as x tends to infinity:
lim(x->∞) -2047476 = -2047476

Therefore, the limit of f(x) as x tends to infinity is -2047476.

Note: The assumption made in this solution is that all the terms in the expansion of the function are real numbers.

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