1. Use the inequalities sinx<x<tanxfor a suitable value ofxto show that pi lies between 3 and 2root3.

2.By writing tanxas sinx/cosx, show that d(lntanx)/dx = 2cosec2x.

3. A tuning fork sounding A avobe middle C oscillates 440 times a second. The displacement of the tip of the tuning fork is given by 0.02cos(2pi x 440t) millimetres, wheretis the time in seconds after it is activated. Find

a. the greatest speed, b. the greatest acceleration of the tip as it is oscillates.

If you know the answers to any of these questions, please, please help!

Thanks!