# How do you evaluate the limit #(x^4-16)/(x-2)# as x approaches #2#?

So:

Hence:

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To evaluate the limit (x^4-16)/(x-2) as x approaches 2, we can use direct substitution. Plugging in x=2 into the expression, we get (2^4-16)/(2-2) = (16-16)/(0). Since division by zero is undefined, we cannot evaluate the limit using direct substitution. However, by factoring the numerator as a difference of squares, we can simplify the expression to (x^2+4)(x+2)/(x-2). Canceling out the common factor of (x-2), we are left with (x^2+4)(x+2). Plugging in x=2 into this simplified expression, we get (2^2+4)(2+2) = (4+4)(4) = 32. Therefore, the limit of (x^4-16)/(x-2) as x approaches 2 is equal to 32.

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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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