A cereal manufacturer claims that there are an average of 200 raisins in each box of cereal. let µ represent the average number
2 answers:
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Answer:
a)∇f = 2y + 2x + 18z
b) =108
Step-by-step explanation:
Given:
f (x,y,z ) =
The curve C :
where 0 ≤ t ≤ 1
Required:
(a) F = ∇f =? (F is a vector here)
(b) =?
Solution
First we will find the directional derivative F = ∇f
for that , we will use the formula :
∇f =
Fx= δf/δx = δ/δx = 2z i
Fy= δf/δy=δ/δy (2xy)j = 2x j
Fz= δf/δz=δ/δz = 18z k
∇f = (2z) i .i + (2x) j.j + (18z) k.k
∇f = 2z + 2x + 18z
<em>For part b):</em>
<em>we will use line integral formula:</em>
to calculate dr, we will need the curve C:
r = x(t)+y(t)+z(t)
r=
=
=
put values of y, x and z
=
=
= (Note : f(1)-f(0))
=2(1)+162(1)+2(0)+162(0)-56
= 2+162 -56
=108