# How do you find the limit of #sqrt(3+x) - sqrt(3)/x # as x approaches 0?

Does not exist.

Since the limits from left and right directions are not the same, the limit of this function is said to be does not exist.

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To find the limit of sqrt(3+x) - sqrt(3)/x as x approaches 0, we can use algebraic manipulation and the concept of limits.

First, let's simplify the expression by rationalizing the denominator. Multiply both the numerator and denominator by the conjugate of the denominator, which is sqrt(3+x) + sqrt(3).

This gives us [(sqrt(3+x) - sqrt(3))(sqrt(3+x) + sqrt(3))]/[(x)(sqrt(3+x) + sqrt(3))].

Expanding the numerator using the difference of squares, we get [(3+x) - 3]/[(x)(sqrt(3+x) + sqrt(3))].

Simplifying further, we have x/[(x)(sqrt(3+x) + sqrt(3))].

Now, we can cancel out the x terms in the numerator and denominator, giving us 1/(sqrt(3+x) + sqrt(3)).

As x approaches 0, the expression sqrt(3+x) approaches sqrt(3), so the denominator becomes 2(sqrt(3)).

Therefore, the limit of sqrt(3+x) - sqrt(3)/x as x approaches 0 is 1/(2(sqrt(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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