Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 6z) k C is the line segment from (2, 0, −2) to (5, 4, 2) (a) Find a function f such that F = ∇f. f(x, y, z) = Correct: Your answer is correct. (b) Use part (a) to evaluate C ∇f · dr along the given curve C.

Required solution (a) (b) 40.

Step-by-step explanation:

Given,

(a) Let,

Then,

Integrating we get,

Differentiate this with respect to y we get,

compairinfg with of the given function we get,

Then,

Again differentiate with respect to z we get,

on compairing we get,

  (By integrating h'(z))  where C is integration constant. Hence,

(b) Next, to find the itegration,

4

Step-by-step explanation:

Here we need to estimated quotient of -23.514 and -3.98.

We need to use the division to find the answer.

Before going to the division, we need to estimate the dividend -23.514 and the divisor -3.98 to nearest integer.

-23.514, here the tenths place digit is 5, since it is greater than or equal to 5, we can 1 in the unit place and round off.

So, -23.514 = -24

-3.98, here the tenths place digit is 9 which is greater than or equal to 5, so we add 1 in the unit place and estimate.

So, -3.98 = -4

Now we have to divide -24 by -4.

Remember, when divide a negative by a negative number, the answer will be in positive. This is a division sign rule.