# How do you evaluate the limit #(sqrt(x+1)-2)/(x-3)# as x approaches #3#?

by Taylor expansion

You can see clearly that the limit is the same as x approaches 3 on both sides as the sign of h is in the error term.

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To evaluate the limit of (sqrt(x+1)-2)/(x-3) as x approaches 3, we can use algebraic manipulation. By multiplying both the numerator and denominator by the conjugate of the numerator, which is sqrt(x+1)+2, we can simplify the expression. After simplification, we find that the limit is equal to 1/4.

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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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