Our function is: . We want to find the limit of this as x approaches 0. The first thing we would want to do is to substitute 0 in for x. But when we do that, we get 0/0, which is undefined:
Let's divide the numerator and denominator both by x:
Now substitute 0 in again:
Because we have a number divided by 0, this cannot exist. If we graph this function (see attachment), we'll also see that the graph diverges at x = 0, so the limit does not exist.
The answer should be D. It is -2 on the inside because it is backwards of what you may think and because it is inside the square root. The -3 represents a down shift of 3
