# How do you evaluate #[(x^2) + 5x + 4] / [(x^2) + 3x -4]# as x approaches -4?

#lim_(x->-4) [x^2+5x+4]/[x^2+3x+4]= lim_(x->-4) (d[x^2+5x+4]/dx)/(d[x^2+3x+4]/dx)= lim_(x->-4) (2x+5)/(2x+3)=(2*(-4)+5)/(2*(-4)+3)= (-3)/(-5)=3/5#

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If you have not yet learned about derivatives and l'Hospital's rule, you can still find the limit.

We can evaluate this limit by substitution. We get

So

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To evaluate [(x^2) + 5x + 4] / [(x^2) + 3x -4] as x approaches -4, we substitute -4 for x in the expression and simplify.

[(x^2) + 5x + 4] / [(x^2) + 3x -4] = [((-4)^2) + 5(-4) + 4] / [((-4)^2) + 3(-4) -4]

Simplifying further, we get:

[16 - 20 + 4] / [16 - 12 - 4] = 0 / 0

Since we have a division by zero, the expression is undefined as x approaches -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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