# What is the domain of the function: #x sqrt(9-x^2)#?

The argument of the square root function must be

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The domain of the function (f(x) = x\sqrt{9 - x^2}) is the set of all real numbers (x) such that the expression under the square root is non-negative. This is because the square root of a negative number is not a real number.

So, we need to find where (9 - x^2 \geq 0).

Solving the inequality (9 - x^2 \geq 0), we get:

[9 - x^2 \geq 0] [9 \geq x^2] [x^2 \leq 9]

Taking the square root of both sides, remembering to consider both positive and negative roots:

[|x| \leq 3]

This means that (x) can be any real number such that its absolute value is less than or equal to 3.

Therefore, the domain of the function is (-3 \leq x \leq 3).

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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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