Question

Can you help me solve this without l'hospital rule http://screencast.com/t/xPTYHbcl

Answer 1

my first thoughts would be to substitute x=1/y
you see we have a formula for x->0
not for x-> infinity with sin function

Answer 2

so, what u get if you put x=1/y ?

Answer 3

cool problem though :)

Answer 4

\[\large \lim_{x \rightarrow \infty} \;\sin\left(\frac{\pi x}{2-3x}\right)\]
This might seem a little strange, but we can pass the limit function into the sine function. Doing so will give us,\[\large \sin\left(\lim_{x \rightarrow \infty} \;\frac{\pi x}{2-3x}\right)\]

Now let's just worry about the limit part, we'll deal with the sine function afterwards.\[\large \lim_{x \rightarrow \infty}\;\frac{\pi x}{2-3x}\]

Do you understand how to find this limit?

Answer 5

we can pass the limit function into the sine function <---reason ?

Answer 6

Ummmm good question, I should probably be able to justify that if I'm going to make a weird move like that. lol