# We have f(x)=x-cubicroot(x+1) Verify that f(sqrt3/9 -1) =(-2sqrt3)/9 -1 and calculate the limit of f(x) as x approaches positive infinity? Thanks!

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To verify that f(sqrt(3)/9 - 1) = (-2sqrt(3))/9 - 1, we substitute sqrt(3)/9 - 1 into the function f(x) and simplify the expression.

f(x) = x - cubicroot(x + 1)

f(sqrt(3)/9 - 1) = (sqrt(3)/9 - 1) - cubicroot((sqrt(3)/9 - 1) + 1)

Simplifying further,

f(sqrt(3)/9 - 1) = (sqrt(3)/9 - 1) - cubicroot(sqrt(3)/9)

Now, let's calculate the limit of f(x) as x approaches positive infinity.

To find the limit of f(x) as x approaches positive infinity, we need to analyze the behavior of the function as x becomes larger and larger.

The function f(x) = x - cubicroot(x + 1) can be simplified to f(x) = x - (x + 1)^(1/3).

As x approaches positive infinity, the term (x + 1)^(1/3) becomes negligible compared to x.

Therefore, the limit of f(x) as x approaches positive infinity is infinity.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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