# How do you find the limit of #[sqrt(x+1) – 2] / [x-3]# as x approaches #3^+#?

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To find the limit of [sqrt(x+1) – 2] / [x-3] as x approaches 3^+, we can substitute the value of x into the expression. By substituting x = 3 into the expression, we get [sqrt(3+1) – 2] / [3-3]. Simplifying this further, we have [sqrt(4) – 2] / 0. Since the denominator is 0, we cannot directly evaluate the expression. In this case, we can use L'Hôpital's Rule, which states that if the limit of the quotient of two functions is of the form 0/0 or ∞/∞, then the limit of the quotient is equal to the limit of the derivative of the numerator divided by the derivative of the denominator. Applying L'Hôpital's Rule, we differentiate the numerator and denominator separately. The derivative of sqrt(x+1) – 2 is 1/(2*sqrt(x+1)), and the derivative of x-3 is 1. Evaluating the limit of the derivatives as x approaches 3^+, we get 1/(2*sqrt(3+1)) / 1. Simplifying this further, we have 1/(2*sqrt(4)) / 1, which is equal to 1/4. Therefore, the limit of [sqrt(x+1) – 2] / [x-3] as x approaches 3^+ is 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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