Determine if F(x, y, z)= yz²i+xz²j+ (2xyz-5)k is a conservative vector field. If it is, find a function f such that F= Vf and use it to evaluate fF.dr along the curve C: r(t) = (3t+1)i-t³j+(4t-1)k where 0≤t≤1.

Q: 7+3.5-11

A: Let's Solve,

Q: 6.4 3

A:

Q: 196. 2(n+1)

A:

Q: 9 b and c

A: b) We check if the denominator is 0 for any value of x.  2x2+5=0 2x2=-5 x2=-5/2 (not possible) So…

Q: Given the parent function f(x) = 2, which graph shows f(x) + 1? -5 -4 -3 -2 2 3 4 2 -5 3 4 2.

A: Given :   f(x)=2x

Q: 6.3 3

A:

Q: 6.1 4

A: Given that  The vector

Q: 12 16

A: We know that If a perpendicular is drawn from the vertex of right angle triangle of a right triangle…

Q: 8 13

A:

Q: 11 35

A:

Q: 4 10

A: Given: The figure,

Q: 14 and 16

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2/5 +7/12

A: Please see the answer below.

Q: 3 power 3

A:

Q: 3(m – 5) + m

A: 3(m-5)+m=0 3m-15+m=0 add both side 15 we get 2m=15

Q: -5 4 -2 -7 -8 2.

A:

Q: 8 15 2 15

A: 8/15 -2/15 here simple substraction given and fraction is given  calculation is given inbelow

Q: k 24

A: First we solve the inequality. ANd for that , we divide both sides by -6 .And on dividing by…