Consider the vector field f(x, y,z)=(2z+5y)i+(z+5x)j+(y+2x)kf(x, y,z)=(2z+5y)i+(z+5x)j+(y+2x)k. a. find a function ff such that f=∇ff=∇f and f(0,0,0)=0f(0,0,0)=0. f(x, y,z)=f(x, y,z)= b. suppose c is any curve from (0,0,0)(0,0,0) to (1,1,,1,1). use part a. to compute the line integral ∫cf⋅dr∫cf⋅dr.

Following are the response to the given question:

Given:

To find:

function=?

line integral=?

Solution:

For point a:

Consider the vector field:

Integrating with respect to

So,  

So,  

Thus,  

For point b:

Learn more:

link

from the sentence, "tomorrow morning, akiko will arrive an hour late" depicts a third person perspective because it doesn't use any pronoun to replace akiko, the subject of the sentence, and it is in singular form since akiko is only one person.