Suppose that a bird flies along the helical curve x = 2 cos t, y = 2 sin t, z = 3t. The bird suddenly encounters a weather front so that the barometric pressure is varying rather wildly from point to point as P(x, y, z) = 6x2z/y atm.
(a) Use the chain rule to determine how the pressure is changing at t = π/4 min.
(b) Check your result in part (a) by direct substitution.
(c) What is the approximate pressure at t = π/4 + 0.01 min?
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