Determine the following limits.
lim x→1 x^3 − 7x^2 + 12x...

Question

Determine the following limits.

lim x→1 x^3 − 7x^2 + 12x / 4 − x

Accepted Answer

Hi, everyone. Let's take a look at this practice problem dealing with limits. This problem says to evaluate the following limit. The limit as X approaches two of the quantity of XQ minus four X squared plus four X in quantity divided by the quantity of five minus X. We're given four possible choices as our answers. For choice A, we have zero for choice B we have three for choice C, we have four, for choice D, we have one. Now we're asked to evaluate the limit as X approaches two of the quantity of X cubed minus four X squared plus or X in quantity divided by the quantity of five minus X. Now, the way we can evaluate this limit is just by setting X equal to two and then evaluating the expression. So this is gonna be equal to too cute minus four, multiplied by two squared plus or multiplied by two. And that quantity gonna be divided by the quantity of five minus two. So now we just need to simplify this expression. We start off by doing the multiplication in the numerator. So this is going to be equal to have two cubed which is eight minus four, multiplied by two squared, which is 16, then we'll have less um, four multiplied by two, which is eight. And then that whole quantity is divided by, we have on the denominator five minus two, which is three. Again, simplifying the numerator, this is going to be equal to, we'll have eight minus 16 plus eight which evaluates to zero and that's gonna be divided by three. And so overall, we'll have zero divided by three, which is equal to zero. So that is the answer that we're looking for. And if I look at my answer choices, this corresponds to answer choice. A so I hope that this explanation has been useful and I'll see you in the next video.

Determine the following limits.
lim x→1 x^3 − 7x^2 + 12x / 4 − x

Key Concepts

Limits

Factoring Polynomials

Indeterminate Forms

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