Find the indicated limit if f(x)=(1)/(2x-8) and g(x)=x^3......... lim(x-4) [f(x)*g(x)]

Question

Find the indicated limit if f(x)=(1)/(2x-8) and g(x)=x^3......... lim(x->4) [f(x)*g(x)]

anonymous · Answer

So far, I know that it simplifies to $$\lim_{x \rightarrow 4} \frac{ x^3 }{ 2x-8 }$$ .... I think ._.

psymon · Answer

Doesnt exist.

anonymous · Answer

Shoot. I figured... Why?

psymon · Answer

So, the idea is you dont want to multiply the functions together, only their limits. So you would normally find the limit of f(x) first, then find the limit of g(x), then multiply the results. Well, f(x) is 1/(2x-8). Clearly x = 4 is undefined. So then the next step is to usually find  away to get the term in bottom to cancel out. But theres no algebra trick you can do to 1/(2x-8) that will prevent it from going to 0 in the denominator. 

Have you seen one-sided limits yet?

anonymous · Answer

I've looked at them a little bit...

psymon · Answer

If you havent been shown them, then there isnt anything more that you can do other than realize theres no way to prevent 1/(2x-8) from going to 1/0.

anonymous · Answer

Okay. It makes sense to me though. I guess I was overthinking. Thanks! (:

psymon · Answer

Yep, np :3