# arcsin

• Nov 11th 2009, 01:08 PM
alexandrabel90
arcsin
may i know how do you find the lim ( x/ arcsin x) as x tends to 0 using sub
y = sin x?
• Nov 11th 2009, 01:37 PM
stapel
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? (Wondering)
• Nov 11th 2009, 02:20 PM
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
• Nov 11th 2009, 02:49 PM
redsoxfan325
Quote:

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 $\displaystyle x=\sin y$. As $\displaystyle x\to 0$, $\displaystyle y\to0$ as well.

Now we have

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