use initial conditions u (0, t) = 0 and u (T, t) = 0 u (0, t) = (c1 + c2) (c4 + c3t) = 0 » (c1 + c2) (c4 + c3t) = 0 %3D u (T, t) = (c1 + cze) (c4 + c3t) = 0 > (ci + cze-*) (c4 + c3t) = 0 this condition is only possible if c1 = c2 = C3 = c4 = 0

Q: Find local max point of f(x,y) = In(x^2 + y^2 + 1). Use gradient descent method. [ Starting point…

A: Given: f(x,y) =ln(x2+y2+1) The given point is (1,1) Learning rate , h=3/2

Q: Calculate the partial derivative of the function f(x, y, z) = xyz at the point (0, 1, 1).

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to (-1, 0,…

A: By Fundamental theorem line integral,we have Where C is curve joining to

Q: Find the partial derivatives fx (3,5) fy (3,5) for the function f(x,y)= y^2/x-y

A:

Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: ag Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7) where g(x,…

A:

Q: If IAIo the equilibrium paintx=0 for the system x-Ax isa stable focus

A:

Q: Find the first partial derivatives of the function. f(x, y, z, t) = 7xyz6 tan(yt) fx(x, y, z, t) =…

A: Given: The function f(x,y,z,t)=7xyz6 tanyt. To find: The first partial derivatives, fx(x,y,z,t)=…

Q: Value of divergence of function (x2y2)î - (z³y 4x) ĵ + 4y² xk at (1, 2, 1) is

A: Given vector is (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: A system of the type i = f(x), f(x) = -gradV(x), is called a gradient system. Investigate the…

A: Given that, A system of the type x˙=fx, fx=-grad Vx is called a gradient system.  Investigate the…

Q: (b) Find orthogonal trajectory of x2 - y = K. (Orthogonal trajectories]

A:

Q: Az Bxm + Cy" – Dx – Ey + 14 where x, y, and z are measured in meter. If you are standing at location…

A:

Q: .    Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to…

A:

Q: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

Q: Explain why the function is differentiable at the given point. 4x f(x, y) = y + sin (0, 6) The…

A:

Q: Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0)  and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: f(x, y, z) = eVx2 + y2, E = {(x, y, z) | 1 < x² + y2 < 4, ys 0, x < y/3, 3 s z 5 4} E = {(x, y, z) |…

A: given fx,y,z=ex2+y2 and a region of integration E=x,y,z|1≤x2+y2≤4 , y≤0, x≤y3 , 3≤z≤4 claim-…

Q: Find the first partial derivatives. (x, y) = xFye-5y ,(X, Y) = ,(x, V) =

A:

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

A:

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: Find the first partial derivatives of at the point (x, y) (1,2). x + y f(x, y) af -(1,2) = 2/3 af…

A: Explanation of the solution is given below...

Q: ih fcuv, w) and its partial derivatives v and w with respecttou and and are Continows that u-x-y, V=…

A:

Q: Correction: Bonus Assignment, Exercise 8: Exercise: 8 Evaluate 1-x²-y² e-3(x²+y²+z²)² dz dydx

A: Given,   from limit we can say this follow x2+y2+z2=1 put this value in integral…

Q: Find all the second partial derivatives. v = sin(3s2 - 4t2) V st Vts Vtt II II

A: As per the guidelines we can solve 3 parts only

Q: Prove that div curl v = 0 where the components of v have continuous second partial derivatives

A:

Q: Find the second order partial derivatives of S(r. y) = (3r +2y) Sm(r, y) = 36(3r + 2y)? Sw (r, y) =…

A: The given two-variable function is: f(x,y)=(3x+2y)4

Q: Q6. Classify critical points of the given plane autonomous system and sketch some trajectories on…

A: Q6. The given equations are,x'=-3x+y2+2y'=x2-y2

Q: Find the first partial derivatives; fx & fy of the function: cos y f (x, y, z) = xz2 cos y. 2 cos y…

A:

Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

A:

Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 0, 1)  and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: ihe fcu,v, w) and its partial derivatives with respect tou and vand w and are Continous that u-メ-ツ…

A:

Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where is player i's…

A: The utility to player 1 is given as: u=xx+n1yAnw-x-n-1y;w&gt;0,A&gt;1 Also, Ak=Aw-x*

Q: Find the 1st order partial derivative of f(x,y,z) = 4x^3y^2 - e^zy^4 + (z^3/x^2) + 4y - x^16

A: The given function is f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16.

Q: Determine the minimum point of fx) =x,²+x,x, +x,² – 3x, – 3x, by using conjugate gradient method,…

A:

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: : Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A:

Q: Find the symmetric equations for the normal line Ly to the surface S: f(x,y)=5√√² + y² at the point…

A:

Q: both first partial derivatives. z = exy %3D az %3D ax %3D ay

A: Solve above problem.

Q: Calculate the partial derivative f2(3,3,1), where f(x, y, z) = xyz. %3D

A:

Q: How are the partial derivatives ∂ƒ/∂x and ∂ƒ/∂y of a function ƒ(x, y) defined? How are they…

A: Consider the provided information, How are the partial derivatives ∂f∂x and ∂f∂y of a function fx,y.…

Q: )The value of partial derivative f-(1,-1,2) of the function f(x, y, 2) - x - Vy2 + z? is: %3D

A: Given function f(x,y,z)=x-y2+z2

Q: Find fz for f(x, y, z) = xcos(y + 3z) + xyz at the point ( 1,3,-1)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Compute the partial derivatives. 6x z = V x2 + y2 az 2 V 2x +y dz ду

A:

Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: Find all the first partial derivatives of z = 3x°y° - 7x°y°. (Choose all applicable answers.) O zy =…

A:

Q: Compute the partial derivative of the function * with respect to z at the point (1,0, 7). Compute…

A:

Q: dN1 =rN1 dt (1-*) - aN1 N2(1 – exp[-bN1]), K %3D dN2 = -dN2+ N2e(1 – exp[-bN1]), dt

A:

Q: x2 - y2 + 2Cx = 0

A:

Q: Calculate the partial derivative f(5, 2, 5), where f (x, y, z) = xyz.

A:

Q: Find the first partial derivatives of the function. f{x, y, z) = x³yz² + 5yz f,(X, Y, 2) = Fy(x, Y,…

A: Here the given function is f(x, y, z)=x5yz2+5yz. We have to find the first partial derivatives fx(x,…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.