Question

If f is the function defined by f(x) = (x - 9) / (x√-3), then lim x->9 f(x) is equivalent to which of the following?

a. 0
b. 9
c. 1
d. Does not exist

Answer 1

The limit as x approaches 9 of the given function does not exist.

Step-by-step explanation:

To find the limit as x approaches 9 of the function f(x) = (x - 9) / (x√-3), we can substitute 9 into the function:

f(9) = (9 - 9) / (9 * √-3) = 0 / 0

Since we have an indeterminate form of 0 / 0, we can try to simplify the expression by factoring and canceling common factors:

f(9) = (x - 9) / (x√-3) = ((x - 9) / (x - 9)) / (√-3)

Now, since x - 9 cancels out in the numerator, we are left with:

f(9) = 1 / (√-3)

However, the square root of -3 is an imaginary number, so the limit does not exist. Therefore, the answer is d. Does not exist.