Show the following limit:

Question

berrymox · Answer

$$\lim_{h \rightarrow 0}\frac{ 1 }{ \sqrt{h+1} +1} = 0.5$$

agent0smith · Answer

Multiply the numerator and denominator by the conjugate of the denominator, which is
$$\large\sqrt{h+1} -1$$

berrymox · Answer

The furthest I got was 1 /[  (sqrt(h+1) -1 ]

berrymox · Answer

I don't know where to go from here

berrymox · Answer

oh wait

berrymox · Answer

I always don't know when to plug-in because I assume I get 0/0 or i >_<

berrymox · Answer

thank you

michele_laino · Answer

it is simple, the function:
$$f\left( h \right) = \frac{1}{{\sqrt {h + 1}  + 1}}$$
is continuous at $h=0$, so please substitute $h=0$, what do you get?

agent0smith · Answer

Oh yeah it's not even -1. Just plug it in as Michele said.

agent0smith · Answer

What I gave you is for if the function was 1 /[  (sqrt(h+1) -1 ]

agent0smith · Answer

"I always don't know when to plug-in because I assume I get 0/0 or i"

If you don't always know... then plug in and find out. In this case if you plug in h=0, you'll discover it is not 0/0.

berrymox · Answer

It's because I try to over simplify, :P