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 6 + 0.01.

Answer with Step-by-step explanation:

We are given that

T(t) be the temperature at time t.

a.Substitute the value of x,y and z

Where

We know that

By using the formula

Now, differentiate w.r.t t

b.

We have to find the approximate value of the temperature at given value of t.

Substitute

Linear approximation formula:

Where

and

Substitute the values

The approximate value of the temperature=

The approximate value of the temperature=

The approximate value of the temperature=

Where

78.59 is the mean

step-by-step explanation:

step-by-step explanation:

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