This problem has two parts but I can only see this so far. I probably over thinking..what is this asking for? How do I answer it?

To evaluate
lim x→ infinity sqrt(x^2 + 4)

*first consider that as x becomes infinitely large

x^2+4 -> __?__

would this just be infinity that they are looking for?

that's correct.

as x gets huge, the 4 is insignificant, so you just have sqrt(x^2) = x.

the program is telling me that is incorrect

nevermind lol thank you

In order to evaluate the limit of the expression lim x→ infinity sqrt(x^2 + 4), you need to determine what the expression x^2 + 4 approaches as x becomes infinitely large.

To find the limit, you can simplify the expression inside the square root as x approaches infinity. As x^2 + 4 contains only an x^2 term, the other terms become insignificant compared to the power of x as x becomes infinitely large.

Thus, you can ignore the constant term 4 as x goes to infinity, and focus only on the dominant term, x^2. As x→ infinity, x^2 also approaches infinity.

Therefore, x^2 + 4 approaches infinity.

So, the answer to the first part of the problem is:

x^2 + 4 -> infinity as x approaches infinity.

Now, you can proceed to evaluate the limit of the original expression lim x→ infinity sqrt(x^2 + 4):

Since x^2 + 4 approaches infinity as x goes to infinity, the square root of (x^2 + 4) also approaches infinity.

Hence, the limit of sqrt(x^2 + 4) as x approaches infinity is:

lim x→ infinity sqrt(x^2 + 4) = infinity.

The answer to the second part of the problem is:

lim x→ infinity sqrt(x^2 + 4) = infinity.