Evaluate the following limits, if they exist.

Question

anonymous · Answer

$$\lim_{x \rightarrow 0^+} \frac{ \cos x }{ \ln x }$$

solomonzelman · Answer

Please don't laugh at me, I am new to this stuff. I am doing my best tough.
 I hate getting disconnected.

The limit will be equal to (on both sides ) to

$\LARGE\color{blue}{ \bf   \lim_{x \rightarrow 0}~\frac{cos(x)}{log(x)}   }$

L'H'S tp derive top and bottom,

$\LARGE\color{blue}{ \bf   \lim_{x \rightarrow 0}~\frac{-sin(x)}{1/x}   }$

and that gives,

$\LARGE\color{blue}{ \bf   \lim_{x \rightarrow 0}~\frac{x(~-sin(x)~~)}{1}   }$                         take it from here.

solomonzelman · Answer

I would plug in zero now, and so yes, the limit does exist at ?

anonymous · Answer

but if I just plug in 1, I get cox(1)/ln(1) = 1/1. So could it equal 1?

solomonzelman · Answer

I wasn't on for a while, so I a just saying that I think that you should plug in zero (not 1, because x->0 that is what the problem says) and plug it in now