# How do you use continuity to evaluate the limit #arctan(x^2-4)/(3x^2-6x)#?

If

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To use continuity to evaluate the limit of arctan(x^2-4)/(3x^2-6x), we can first simplify the expression by factoring out a common factor of x from both the numerator and denominator. This gives us arctan(x^2-4)/(3x(x-2)).

Next, we can evaluate the limit by plugging in the value that x approaches into the simplified expression. In this case, we are interested in finding the limit as x approaches a certain value, let's say c.

To evaluate the limit, we can use the fact that the arctan function is continuous for all real numbers. This means that we can evaluate the limit by directly substituting the value c into the expression. So, we substitute x = c into the simplified expression:

arctan(c^2-4)/(3c(c-2))

By doing this, we obtain the value of the limit as x approaches c.

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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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