sin(7y), 8x2+7x°cos(7y)). vative servative n of the parabola y=x2-16 from (4,0) to (-4,0). Which of the following statements are true? (Select all tl ental Theorem of Line Integrals, F-dr = f(-4, 0) – f(4, 0), where f(x,y) is a potential function for F. %3D e of path, F.dr = F-dr, where C' is the line segment from (-4, 0) to (4, 0).

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

Q: (b) Verify that the following function is harmonic u(x, y) = −e sin x - 2e-siny. Find a harmonic…

A: Here we have to verify that the function is harmonic and then find the harmonic conjugate.

Q: ind the fangent line for... 1x1) = +²+et ( (1) = sh (k) + t at t=0 B) r(e) = sinG + case at 6: T

A: Explaination of the answer is as follows

Q: 7. (~Ch16 Review #6) Compute y3 dx + x² dy where C is the arc of the parabola x = 1- y² from (0, –…

A: In this question we need to find the given line integral .

Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

Q: d dx y' z' y" z"

A:

Q: (z)dz

A:

Q: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

A:

Q: tion 16 of 17 Let P be the tangent plane to the graph of g(x, y) = 18 – 9x - 18y at the point (4,…

A:

Q: 7. F- dr from (0,0) to (3,9) along the curve y=x' if F(x, y, z) = 4 xyi + 3xy'j Evaluate

A:

Q: Use the Cauchy-Riemann Equations to show that f(z) = z Im(z) is only differentiable at z = 0 and…

A:

Q: Does f(z)=z/(sin z)^2 have a pole of order 1 or 2 at z=0?

A: f(z)=zsin2zFor the poles first we look at the zeros of the denominatorat z=0 We know sin(z) has a…

Q: Find the arclingth of A) r(6) = 4cos (0) OS OS T ... B) / X (²) = +²+1 2 y(t) = 2³² +2 1≤t≤ 3

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.