Determine order and degree * d'y d'y + cos dr? dr? 2 O 5 undefine- Not linear

Q: Find the work done by the force F = 4xyi + (2x² – 3xy)j by pushing a particle along the line segment…

A:

Q: What is the equation of the tangent plane to the surface y = eª cos (z) at the point (1, e, 0)?

A:

Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (5,2,0) on the…

A: The equation of the surface is -cosπx+2x2y+4exz+4yz=105. The function is fx, y,…

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

A:

Q: Find the parametric equation for a line that is tangent (intersection) of the two fields below: −2x…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: sin t cos t dt Jo

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: Show that if the function f(x, y) = ex siny + ecosx, satisfies Laplace Equation.

A: We can solve this as follows:

Q: sec 2x da 4. I+3 tanzx

A: Integration methods help to find the answer to the problem. Substitution of the function helps to…

Q: where does this concave up and down?

A: A graph is concave up if f''x>0 and concave down if f''x<0. When f''x>0, it means…

Q: Determine the equation of the tangent plane to the surface z = cos(x + 2y) at the point (2,-1,0).

A: Tangent plane to f(x, y) at (x0, y0) is given by below:

Q: Each of the two functions v and u with the variables x and y satisfy he Cauchy - Riemann equations,…

A: Let,  u=x2-y2, v=2xy

Q: Find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis

A: We have to find the moment of inertia of the area of the loop y2=x2(1-x), with respect to y-axis.

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

A:

Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

Q: Write an equation in general form of the tangent plane to the surface x^2+siny + z^3 = −4 at the…

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

A:

Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

A:

Q: plot parucul Solu 1. y" +3y' – 4y= sin wx, 2. y" +3y' – 4y = cos wx.

A:

Q: b) Use chain rule 1 - arctan u, where u = e* y =

A: Given y=1u - arctan u, where u=ex apply derivatives on both sides…

Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

A:

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: c. Based on the orientation of your rectangle would we integrate with respect to x or y? С.

A: Follow the procedure given below.

Q: find fsub(x), fsub(y), and fsub(z): f(x,y,z)=e^yz+sinx)

A: Given,          fx,y,z=eyz+sinx

Q: compute using the parametric equations I= cost, y = sin t, te (-x, 0) Write as a function (i) of t.…

A: Using chain rule,

Q: 5, find dt when r = 3. dt Let A be the area of a circle with radius r. If %3D %3D

A:

Q: (c) curve y = 5-x", line y=x+3 (d) y= sinx, y=cosx, x= 7 /4, x=7/2

A: Double integers

Q: ue of J. Note that the lows

A: Given ∇.V=1r2∂∂rr2vr+1rsinθ∂θ∂∂θsinθvθ+1rsinθ∂vϕ∂ϕ

Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

A:

Q: cotu. vX + vy + y %3D If u = show that x ax ay = CoS coS х - у

A:

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

A:

Q: What is the moment of inertia of this area about the line y = -10 ?

A:

Q: = (u² - cos v, u + sint, cos v) x(u, v):

A:

Q: The linear approximation to f(x, y) = /2y + cos2(x) at the point (0,0) takes the form Ax + By + C.…

A:

Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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

Q: The plane tangent to the surface z +1= re" cos z at (1,0,0) can be represented by the equation X + y…

A: Given: z+1=xey cosz

Q: 2dy -2y 2. zt at

A: Solved below

Q: u =1-1,y=6-2+름 x = 1-, y = 6-

A: We have given parametric equations x=1-1t, y=6-7t+2t2. First, evaluate the first derivative dydx. To…

Q: are two linearly independer d'y 3dy equation dx? dx

A:

Q: Find an equation for the tangent plane to the surface z +4 = ry" cos(2) at the point (4, 1, 0).

A: Use the partial differentiation for finding the tangent plane.

Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Find equations for the tangent plane and the normal line at point Po (Xo Yo.Zo) (5,2 on the surface…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Given:…

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

A:

Q: Integrate h(x, y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0). goes along the x-axis…

A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

Q: Determine the linearization of f(x, y) = arctan(x² + y²) at

A:

Q: integrate ƒ over the given curve. ƒ(x, y) = x2 - y, C: x2 + y2 = 4 in the first quadrant from (0, 2)…

A: The given curve C is a circle with center at origin and radius of 2 units. Let the parametric…