# How do you find the limit of the piecewise function #f(x)={(x^2,if x text{ is rational}),(0,if xtext{ is irrational}):}# as x approaches 0?

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To find the limit of the piecewise function f(x) as x approaches 0, we need to consider the limit of the function for both rational and irrational values of x.

For rational values of x, the function f(x) is defined as x^2. Therefore, as x approaches 0, the limit of f(x) for rational values is 0^2, which is 0.

For irrational values of x, the function f(x) is defined as 0. Therefore, as x approaches 0, the limit of f(x) for irrational values is 0.

Since the limit of f(x) is the same for both rational and irrational values of x, the overall limit of the piecewise function f(x) as x approaches 0 is also 0.

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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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