# How do you find the limit of #((sqrtx+4)-3)/(x-6)# as x approaches 6?

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To find the limit of ((sqrtx+4)-3)/(x-6) as x approaches 6, we can use algebraic manipulation and the concept of limits. By factoring the numerator as (sqrtx+4-3) and simplifying, we get (sqrtx+1)/(x-6). Next, we can simplify further by multiplying both the numerator and denominator by the conjugate of the numerator, which is (sqrtx+1). This results in ((sqrtx+1)(sqrtx+1))/(x-6)(sqrtx+1). Simplifying this expression gives (x+1)/(x-6)(sqrtx+1). Now, we can substitute x=6 into this expression to find the limit. Plugging in x=6 gives (6+1)/(6-6)(sqrt6+1), which simplifies to 7/0. Since the denominator is 0, the limit does not exist.

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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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