# How do you find the limit of #(x²-25)/(sqrt(2x+6)-4)# as x approaches 5?

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To find the limit of (x²-25)/(sqrt(2x+6)-4) as x approaches 5, we can use algebraic manipulation. First, we factor the numerator as (x+5)(x-5). Then, we simplify the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is sqrt(2x+6)+4. This results in ((x+5)(x-5))/((sqrt(2x+6)-4)(sqrt(2x+6)+4)). Simplifying further, we get (x+5)/sqrt(2x+6)+4. Now, we can substitute x=5 into the expression to find the limit. Plugging in x=5, we get (5+5)/sqrt(2(5)+6)+4, which simplifies to 10/4. Therefore, the limit of (x²-25)/(sqrt(2x+6)-4) as x approaches 5 is 10/4 or 2.5.

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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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