# How do you find the limit of #(x^2-5x+4)/(x^2-2x-8)# as #x->4#?

Factor, simplify and try again.

When we try to evaluate by substitution, we get

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To find the limit of (x^2-5x+4)/(x^2-2x-8) as x approaches 4, we can substitute the value of 4 into the expression and simplify. By doing so, we get (4^2-5(4)+4)/(4^2-2(4)-8). Simplifying further, we have (16-20+4)/(16-8-8), which becomes 0/0. This is an indeterminate form. To evaluate the limit, we can factorize the numerator and denominator. Factoring the numerator gives us (x-4)(x-1), and factoring the denominator gives us (x-4)(x+2). Canceling out the common factor of (x-4), we are left with (x-1)/(x+2). Now, substituting the value of 4 into this simplified expression, we get (4-1)/(4+2), which equals 3/6 or 1/2. Therefore, the limit of (x^2-5x+4)/(x^2-2x-8) as x approaches 4 is 1/2.

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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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