Hey I have a problem with limits.

In my example, I have: lim(sinx * cosx - sinx)/x^3 , as x-0

then it becomes equal to: lim(sinx/x) * (cosx-1)/x^2

My question is: how did he go from sinx * cosx - sinx to cosx - 1.

I'm thinking it's an identity but cannot find it. Any insight would be much appreciated.

Question

Hey I have a problem with limits.

In my example, I have:  lim(sinx * cosx - sinx)/x^3 , as x->0

then it becomes equal to:  lim(sinx/x) * (cosx-1)/x^2

My question is: how did he go from sinx * cosx - sinx     to   cosx - 1.

I'm thinking it's an identity but cannot find it. Any insight would be much appreciated.

anonymous · Answer

$$\lim \frac{ \sin(x) \cos(x) - \sin(x) }{ x^{3} } $$  as x-> 0

anonymous · Answer

to:
$$\lim \frac{ \sin(x) }{ x } * \frac{ \cos(x)-1 }{ x^{2} }$$

anonymous · Answer

How did my example jump to this equation?

psymon · Answer

All that was done is a sin was factored out. sinxcosx - sinx just became sinx(cosx-1). As for the splitting of fractions, theres no identity, its just a visual. It was written ina different way so you can maybe see whats going on. Because for example, sinx/x as x goes to 0 is an identity and it equals 1. But you might not see that unless its written in that way.

anonymous · Answer

oh

anonymous · Answer

OMG thanks so much psymon hahahahaha i love you!

psymon · Answer

yeah, np :3