The function is:

__(tan(x))^3 - x__

x+x^2

Allowed facts to use are that the limit as x tends to 0 of sin(x)/x=1, and theorems including the algebra of limits, sandwich theorem and the 'changing the variables' theorem.

I believe the limit to be -1, and I'm confident of showing it using the thorems stated above, so my problem isn't specifically with showing the limit, it's more with formatting the problem. Re-writing the initial function in such a way that I can use the limit of sin(x)/x.

I started by taking (tanx)^3= (sin(x)^3)/(cos(x)^3), and then (cos(x))^3= cos(x)(1-(sin(x))^2). But to be honest it all gets rather complex, and as I haven't learnt Latex yet it would look an absolute mess on here, and also my trigonometry is a bit rusty, so if anyone could help me through this initial part, or offer an easier method, I'd be grateful. Thanks!