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

Please see below !

Or if it as you said approaches to 2 So, the answer is D.N.E (doesn't exist

look at the graph

SO IT DOEN't exist.

graph{(3x^2+x6)/(x^2-4) [-8.38, 11.62, -9.28, 0.72]} )

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To find the limit of (3x^2+6x)/(x^2-4) as x approaches 2, we can substitute the value of 2 into the expression. However, this would result in division by zero, which is undefined. Therefore, we need to simplify the expression by factoring the denominator. The denominator can be factored as (x+2)(x-2). Canceling out the common factor of (x-2) in the numerator and denominator, we are left with 3x/(x+2). Now, substituting x=2 into this simplified expression, we get 3(2)/(2+2) = 6/4 = 3/2. Therefore, the limit of (3x^2+6x)/(x^2-4) as x approaches 2 is 3/2.

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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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