# How do you find the limit of #sqrt(x+1)/(x-4)# as x approaches 3?

Let's try direct substitution.

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To find the limit of sqrt(x+1)/(x-4) as x approaches 3, we can substitute the value of x into the expression. However, this results in an undefined expression since it leads to division by zero. To evaluate the limit, we can simplify the expression by multiplying both the numerator and denominator by the conjugate of the denominator, which is (x-4). This simplifies the expression to sqrt(x+1)*(x-4)/(x-4)*(x-4). Canceling out the common factor of (x-4), we are left with sqrt(x+1)/(x-4). Now, substituting x=3 into this simplified expression, we get sqrt(3+1)/(3-4), which simplifies to sqrt(4)/(-1). The square root of 4 is 2, so the limit is -2.

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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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