Someone PLEASE help me. lim x-4 = (1/sqrt(x)-2) - (4/x-4)

Question

Someone PLEASE help me. lim x->4 = (1/sqrt(x)-2) - (4/x-4)

jim_thompson5910 · Answer

Plug in x = 4 and you'll find that you have $$\large \infty-\infty$$ which is an indeterminate form, what does that mean?

anonymous · Answer

L'hospital!!!!!!

anonymous · Answer

Don't you have to rewrite the problem?

anonymous · Answer

What is L'hospital?!

anonymous · Answer

pretty sure he doesnt apply in this situation, but i think of him every time i see limits

jim_thompson5910 · Answer

exactly, you have to write the RHS into the form $$\large \frac{f(x)}{g(x)}$$

jim_thompson5910 · Answer

unfortunately it doesn't work in all cases, be nice if it did

anonymous · Answer

There is an actual answer to this though, not just indeterminate.

jim_thompson5910 · Answer

which is why you need to get it into $$\large \frac{f(x)}{g(x)}$$ form and apply L'Hospitals rule

anonymous · Answer

rewrite  (1/sqrt(x)-2) - (4/x-4) in the form of (x-4)-(4*(sqrt(x)-2))/(sqrt(x)-2)*(x-4), the apply Hôpitals rule, which is to differentiate both sides and then take the limit