Question

True or False?
f(x)—> +infinity as x—> 2 for the function f(x)=1/(3x-6)

Answer 1

Answer:

False

Step-by-step explanation:

Keep in mind both the right and left-side limits of a function have to be equal to each other in order for the limit of the function to exist:

Right side limit: $\lim_{x \to 2^{+}} \frac{1}{3x-6}=\infty$

Left-side limit: $\lim_{x \to 2^{-}} \frac{1}{3x-6}=-\infty$

Because both side limits do not equal $\infty$, then the limit does not exist, which means that the statement is false.

You can also see this visually on a graph if you'd wish to plug in the function