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Hi, I really need help on these problems:
1. A point P moves along the curve in such a way that the y-coord is increasing at a constant rate of 0.06 units per second. Find the rate of change of the x-coord when P passes through (2,5).
2. A curve is such that dy/dx = sqrt(4x+1) and (2,5) is a point on the curve. Find the equation of the curve.
3. Show that (d^2y)/(dx^2) * (dy)/(dx) is constant.
4. Find the volume obtained when the shaded region is rotated through 360 degrees about the x-axis. Give you answer in terms of pi.
5. Part of a curve y=x/2 + 6/x is shown. The line y=4 intersects the curve at the points P and Q. Show the tangents to the curve at P and Q meet at a point on the line y=x.
Please help, I am quite clueless.
Solution