SOLUTION: Solve the following limit: lim x→4 (x^2 − 4x/ x^ 2 − 16)

Question 1174500: Solve the following limit:
lim x→4
(x^2 − 4x/ x^ 2 − 16)
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

For a moment, let's completely ignore the limit portion or limit notation.

Let's focus on the expression only. So we'll focus on

Simplifying the expression leads to:

Such a simplification is necessary because plugging x = 4 into the original expression leads to a division by zero error
Note how x^2-16 = 4^2 - 16 = 16 - 16 = 0 would be in the denominator if x = 4.

But with the simplified expression , we can plug in x = 4 just fine
Doing so gets us

As x gets closer and closer to x = 4, the value of gets closer and closer to y = 1/2 as we apply the limit. As with all limits, we don't actually arrive at the exact value. We only get closer.

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Answer: 1/2

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