Suppose that the temperature at the point (x, y, z) in space is t(x, y, z) = x2 + y2 + z2.

let a particle follow the right-circular helix

σ(t) = (cos(t), sin(t), t) and let t(t) be its temperature at time t.

(a)what is

t '(t)?

t '(t) =

(b)find an approximate value for the temperature at

t =

π/
2
+ 0.01