Question

Solve 74 (make sure to solve for the limits and find the asymptotes)

Answer 1

Given the function:

`f(x)=x^2(4x^2-√(16x^4+1))`

You need to remember that, by definition, the Domain of a Radical Function contains all the possible values of "x" that makes the square root positive.

In this case, you can identify that exponent 4 of the variable inside the square root will make every value of that "x" a positive value, and the number 1 that is added is also positive. Therefore, this square root will be always positive. This means that:

`Domain:All\text{ }Real\text{ }Numbers`

By definition, a Vertical Asymptote is a value of "x" that is not in the Domain of that function.

Since the Domain on this function is all Real Numbers, you can determine that there is no Vertical Asymptote.

Hence, the answer is: There is no Vertical Asymptote.