# How do you evaluate the limit #(x^4+5x^3+6x^2)/(x^2(x+1)-4(x+1))# as x approaches 1?

Plugging in

Generally, plugging in the value you're approaching is the first step you should take when working with a limit unless you know beforehand you'll be working with an indeterminate form:

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To evaluate the limit, we can simplify the expression first. Factoring the denominator, we get (x^2 - 4)(x + 1). Canceling out the common factor of (x + 1) in the numerator and denominator, we are left with (x^4 + 5x^3 + 6x^2)/(x^2 - 4). Plugging in x = 1 into this simplified expression, we get (1^4 + 5(1)^3 + 6(1)^2)/(1^2 - 4) = (1 + 5 + 6)/(-3) = 12/-3 = -4. Therefore, the limit of the given expression as x approaches 1 is -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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