nd the function P(a.y) which Satisfics Laplace a rectangle Pan +Fyy =0 shich also Satisfied the boundany Conditions P(x,0) = 0, P(x,b) =0 in %3D 9(0,y)=0, P(0.y) = fly) cohère fly). is the given fun" osysb.

Q: Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to…

A:

Q: 3. Let f(x, y) = zsin ry. Find: (a) f(x, y) (b) f(x,y) (c) Syy(x, y) (d) fyz(x, y)

A: Given function is f(x, y) = x sin(xy)

Q: Given: A(-2,2), B (1, –2), C (4, 3) Using a scale factor of , AABC is dilated from the origin to…

A: The coordinates of the Vertex of ∆ABC A(-2,2); B(1,-2); C(4,3),  we have scale factor  52,

Q: Please do 4

A: 4. (a) To Evaluate: ∫C​x ds, where C is the arc of the parabola y=x2 from (0,0) to (1,1). Let x=t,…

Q: A) Link between plane and line in the differentiation. 7) Find the aquations of alono pocinh the…

A: Link between line and plane.

Q: Let f(x.y) = ry. a. Sketch/describe the domain of g Domain = { (x,y)]yz0} b. Sketch a contour map…

A:

Q: 29. f(x, y) = x + y, C: x? + y² = 4 in the first quadrant from (2, 0) to (0, 2)

A:

Q: Consider the exact U (x,y) that 2x + f = x taf Statistics. au aa au DDE (2x+ f) dx + (x + ² f) df =…

A:

Q: 4. §13.3. Q49. Consider function w=w(x, y, z). (a). Find Ow/dx. (b). Find Ow/ay. (c). Find əw/az. w…

A: Given function-We have to find the partial derivatives.

Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

A:

Q: Find the normal and osculating planes of the given function at the point r (t) = (4t 1, t² +t,…

A:

Q: Evalwate f, the inaicated point. (Y.y) and Fy y,y) CY.y) at 3. at (l,3)

A:

Q: 1) Find the limited Zone of curves piven! area the remaining bet ween the 2. y = 9= x² and

A:

Q: 3. Given F(x,y)=(y,2x), find F-T ds where curve C is the parabola y=x from point (0,0) to point…

A: We use line integration to evaluate this.

Q: as Let ĝ +sinh (z?) - ji = 27 where w=f (x,y,2)- %3D Find 2 nd JW and au

A: In the given question we have to find the partial derivatives of with respect to x ,y and z. here we…

Q: zek whe ther 7,4)=(2+) 2) %3D nes a lince tras Jov Me

A:

Q: Determines the distance between the left right.

A:

Q: Find the isogonal trajectories cutting at an angle of arctan 4 to the family of curves y = Inx + C.

A:

Q: Q1\ Find the extremals of functionality

A: Given,            Jy=∫x1x2xy'2-yy'+ydx

Q: Find the direction in which the given function is increasing most rapidly at the point P, (-2, –1,…

A: Given function f(x, y, z) = x√(y² + z²) We have find the direction in which the given function is…

Q: I, Use Stoke's theorem to evalueate S.Fidr, where F Cau2)= - it +x3 + 2î aind C is the Ceurve of…

A:

Q: xye-(2²+v²+z*). Find all points (x, y, z) such that Vf(x, y, z) Question 2. Consider the function…

A:

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: state the arder, degree, and linearity of the filowing differe ntial squtions ) ax* 9 + asx) : 3x-4…

A:

Q: Find the length of the curve y? = (x – 2)° between the points (2, 0) and (4, 2/2). 22/22 – 2/2 a)-…

A:

Q: A Find the value of J G dL if G = x'a, - xyza, given points P,(1,2,3) and P;(5,0,4) and a path…

A: Given: G=x2ax-xyzaz P1:1,2,3 P2:5,0,4   To find: The value of ∫P1P2G·dL for a path consisting of:…

Q: Evaluate the length of the curve x = 6 – Vy – 2 , 3< y<6

A: To find the length of following curve  x = 6 - sqrt( y - 6) 3 ≤ y ≤ 6

Q: Find fyzy. 9,8 f(x, y) = x°y³ – 8x*y + x f yry yxY ||

A:

Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: 17. Let foxys = exy. Find the equation for the tangent plane to the graph of f at the point (1.1).

A:

Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

A:

Q: Which of the following is the tangent plane to z = 2x² + y² at the point (1, 1, 3)? z = 4x + 2y z =…

A:

Q: Examine the behavior of f(r, y) as (z,1) approaches (0,0) along straighe lines chrough the origin.…

A:

Q: 7. If F = (yz,-2xz,xy), the value of ||F.n dS , where S is a sphere of radius a centered at the…

A:

Q: find the line ariz ation of the followwing function. fcx, y>=J 9z*+I6y² point (1,1). Use what this…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.