Consider f and c below. f(x, y, z) = yzexzi + exzj + xyexzk,

c. r(t) = (t2 + 5)i + (t2 − 3)j + (t2 − 5t)k, 0 ≤ t ≤ 5 (a) find a function f such that f = ∇f. f(x, y, z) = (b) use part (a) to evaluate c f · dr along the given curve

c.

We're looking for a scalar function such that . This means

In the second PDE, integrate both side with respect to :

Differentiate both sides of this with respect to :

Differentiate this with respect to :

for some constant , so that

By the fundamental theorem of calculus, this line integral has a value of

since

well we know there are 4 clubs in 52 cards so it’s replaced so it should be 3/51

step-by-step explanation:

i get you, what you should do is think of the positive things that would come out of it. it will make yours parents proud and raise your grade. you should always try and if you can't focus tell the teacher.