# Math Help - arcsin

1. ## arcsin

may i know how do you find the lim ( x/ arcsin x) as x tends to 0 using sub
y = sin x?

2. Does "using sub y = sinx" mean that you are supposed to use a substitution, such as "x = sin(y)"...? Are you familiar with l'Hospital's Rule?

3. no. i haven learn l'hospital rule. but from my notes, the hint given for this question is use substitution...

so im not sure if it is sub y= sin x or x= siny..but it should be the same

4. Originally Posted by alexandrabel90
no. i haven learn l'hospital rule. but from my notes, the hint given for this question is use substitution...

so im not sure if it is sub y= sin x or x= siny..but it should be the same
Let $x=\sin y$. As $x\to 0$, $y\to0$ as well.

Now we have

$\lim_{x\to0}\frac{x}{\arcsin x}=\lim_{y\to0}\frac{\sin y}{y}$