Let f(x, y) = 160 2x2-3y² 2a? – For which value(s) of y is f(4, y) = 10? y =

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: Let f(x, y) = 12x² + 7y² + 3x + 3y+ 6 Find D = frz · fy – fåy-

A:

Q: - f(x, y) = Vx5 + y5. Find f-(0, 0).

A: Given that fx,y=x5+y55.It is required to find fx0,0.

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7. fxy(x,y)=

A: Concept: Partial derivatives: In differential geometry and vector calculus, the partial derivative…

Q: 2x –1 1 , show that y"+ y' + xy +1 c) If y =-

A:

Q: f(x, y) = x + y' subject to x + 4y = 29 occurs.

A:

Q: b. min f (x, y) = 3x² – y² s.t. 2х — 4у 3D —11

A: Minimum value of function is determined using lagrange multiplier and its value is -33/4.

Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: If f(x,y)=xe"*/2+135x?y3, then əx²əy³ at (1,1) is equal to

A:

Q: [F-dš where F = xỉ – y°j+(x+ y+z)k

A:

Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: Y Is the midpolnt of XZ.If XZ 8x-4 and YZ = 3x +1, find x.

A: Given Y is the mid-point of line segment XZ XZ = 8x-4 YZ = 3x+1   to solve the given question use…

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

A:

Q: Solve for the domain and range of. f(x,y,z) = %3D V4-x2-y²

A:

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,2,4), and use it to 2 %3D…

A:

Q: If f(x,y.z)= In(x2 +y³ +2z5), Find and dx² dz2

A:

Q: Determine the relative extrema of f(x, y) = 2x2 + y2 + 8x − 6y + 20.

A:

Q: Suppose that f(x, y) = y/x³ + 1 at which {(x, y) | 0 < y < x < 1}. %3D D

A:

Q: Find fxy(x,y) if f(x,y) = (x5+y³) 7. fxy(x,y) =

A:

Q: 4. Sketch: (a) f(x, y) = 4 – x² – y? f (x, y) = x² – y² + 2x ** (b) (c) f(x, y) = /A– x² – 4y² f (x,…

A: 4. (a) We are to sketch the graph of the function f(x,y)=4-x2-y2 \

Q: Se-2t if 0 3,

A:

Q: Find fxy(x,y) if f(x,y) = (x² + y²)6.

A:

Q: .Determine if F(x, y) = (2xy + y-2)i + (x² – 2xy-3)j for y > 0 is conservative.

A:

Q: 6x + 17y df f f(x,y) then i : 6x 17y ду 204x (6а — 17у)? - 204x - (бх — 17у)? 204x (6x + 17y)² 204x…

A:

Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

A:

Q: Find fxy(x,y) if f(x,y)= e 8xy² fxy(x,y)=

A:

Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

A:

Q: f(x, y) = Calcule fzz 3ze + 9y + E O 3e" O 3ye" O 3ze"

A:

Q: 2. Differentiate the follow a) y = e 2x -ex %3D ex

A:

Q: Let f(x,y) = 10x^3y^4+ 21xy^2 Find ?yyy

A:

Q: Find fr, fu, and f.. -0.5 f(x, y, z) = (4x² + 6y² + 3z²) fz = fy = f: =

A:

Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

A:

Q: dy If dz 3x - 3 and y(0) = 8, then y(1) %3D ---

A:

Q: F(x,y, z) = 5x² + 2y² + 4xy + xz

A:

Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

A:

Q: Find the function​ y(x) satisfying d3y/dx3=36, y′′(0)=14, y′(0)=5, and y(0)=8.

A:

Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

A:

Q: 2x2 f' (æ) = If f(x) = V 1+t° dt, then

A: To find the derivative of integral apply the follow rule

Q: or f(x, y) a + y? – xy +1 -

A: Consider the given function as fx,y=13x3+12y2-xy+1

Q: Q3: 1f f (x,y) = 6x*y5 + 4x*y4 Prove that: f (x,y) * fxxyy fxx * fyy = 1

A:

Q: Find fxxy given that f(x, y) = e^xy^2

A: Given,   f(x,y)=e^x *y^2             we have to find fxxy

Q: Find fyæy. f(x, y) = a*y® – 4x°y + x 4.6 3. -

A:

Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

A:

Q: Q4. Find the values of the constants a, b, c so that - - F = (axy + bz³)i + (3x² − cz)j + (3xz² –…

A:

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

A:

Q: 0If z-x"f), show that xZ+JZy=mZ.

A:

Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

A:

Q: Solve for the domain and range of. f(x,y,z) = V4-x2-y?

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.