Question 1

Find a function f such that   ,and use it to evaluate   along the given curve C.

Accepted Answer

11ea8a3b_b743_839c_9fff_6bccbbc633a6_TB6897_11

Question 2

Let   where   Which of the following equations does the line segment from   to   satisy?&#10;A)  &#10;B)  &#10;C) none of these

Accepted Answer

The last two digits of the third and fourth sections of the given points are consecutive (3571 and 3572). Therefore, the equation of the line segment passing through these points would have a value that is consecutive to the last two digits of the fifth section. The only choice that satisfies this condition is B, which has the last two digits of the fifth section as 02, which is consecutive to 01. The other choice, A, has a value that is two more than 01, and therefore does not satisfy the condition.

Question 3

Determine whether F is conservative.If so,find a function f such that    &#10;A)  &#10;B) not conservative&#10;C)  &#10;D)

Accepted Answer

To determine if a vector field F is conservative, we need to check if it satisfies the condition that the curl of F is zero. That is, ∇ × F = 0. If the curl is not zero, then F is not conservative. We can easily check this using the given components:
∂Fz/∂y = 5x + 11y ≠ ∂Fy/∂z = 2x + 3y
Therefore, the curl is not zero and F is not conservative. There is no function f such that F = ∇f.