Ok, I am studying some practice problems for an upcoming exam. I seem to be having some issues with this section and making sense of the rules.

I have this example:

Lim x--> 1

(x-1)
_________
sqrt(x+3) -2


Plug in 1, obviously that will not work. I see limit calculators say the numerator is 1/1 and the denominator is now 2*sqrt(x+3)

Can someone explain this rule to me? It seems you divide the top by 1, and times the denom by the 2. I would think this would mean the answer is 1/4, not 4. Where did the 1/1 go?

I don't know why whatever source you are using provides that answer - it's incorrect. Are you familiar with l'hopital's rule? Replace the numerator and denominator by their derivatives, and then find the limit of the new fraction as x -> 1. What you should find is the numerator becomes 2 \sqrt {x+3}, and the denominator becomes 1.

Yo

Basically, limits at domain points ask what happens when you get really close to something. If your function is reduced all the way (which it is) you just have to check and see if the top is also set to zero. If it is you do not have a vertical asymptote and simply plug in a really close number (0.999999) to see what happens there.

Might want to try out simplisico, that's how I got it, they are really helpful

Og


Yo

Basically, limits at domain points ask what happens when you get really close to something. If your function is reduced all the way (which it is) you just have to check and see if the top is also set to zero. If it is you do not have a vertical asymptote and simply plug in a really close number (0.999999) to see what happens there.

Might want to try out simplisico, that's how I got it, they are really helpful

Og

And I need 5 more chars