How do you find the limit of #(x^3 *abs(2x-6))/ (x-3)# as x approaches 3?
The one sided limits disagree, so there is no two sided limit.
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To find the limit of the given expression as x approaches 3, we can use algebraic manipulation and the properties of limits. First, we simplify the expression by factoring out common terms:
(x^3 * abs(2x-6))/ (x-3) = (x^3 * abs(2(x-3)))/ (x-3) = x^3 * abs(2)
Next, we can evaluate the limit separately for each term. As x approaches 3, the absolute value term remains constant at 2. The limit of x^3 as x approaches 3 is 3^3 = 27.
Therefore, the limit of the given expression as x approaches 3 is 27 * 2 = 54.
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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.
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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