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

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To find the limit of (2x^2 + x + 1) / (x + 2) as x approaches 2^-, we substitute the value of x into the expression.

(2(2^-)^2 + 2^- + 1) / (2^- + 2)

Simplifying this expression, we get:

(2(1/4) + 1/2 + 1) / (1/2 + 2)

(1/2 + 1/2 + 1) / (1/2 + 2)

(2/2 + 1) / (1/2 + 2)

(1 + 1) / (1/2 + 2)

2 / (1/2 + 2)

To further simplify, we need to find a common denominator:

2 / (1/2 + 4/2)

2 / (5/2)

Multiplying by the reciprocal, we get:

2 * (2/5)

4/5

Therefore, the limit of (2x^2 + x + 1) / (x + 2) as x approaches 2^- is 4/5.

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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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