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

wth is with the little mtn top and what are you talking about like fix your words and accually make sence with them and i like was in a completly different question like three times like it seems like your ilitteret

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.