Question: A triangle is formed using as vertices the origin, the point ( x , 0), \(0\le x\le \pi \), and the point \(\left( x,x\sin x \right)\)

1. At what rate is the height of the triangle increasing or decreasing (the base is along the x-axis) when \(x=\pi /2\) and x is increasing at a rate of 3 units per second?
2. At what rate is the area of the triangle increasing or decreasing when \(x=3\pi /4\) and x is increasing at the rate of 2 units per second?
3. At what rate is the distance from \(\left( x,x\sin x \right)\) to the point (0, 0) is changing when \(x=\pi \) and x is increasing at a rate of 4 units per second?

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