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

Q: If f(x,y,z)=xe^{4y}\sin(6z), then the gradient is

A:

Q: ive of f(x, y, z) 1) in the dired

A:

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

A:

Q: compute ∫_∂D(x^2ydx+xy^2dy, where D is described by 0≤x≤1, 0≤y≤x

A:

Q: If F(x)=sinx+6x2−4 is an antiderivative of f(x) then f(x)=

A: If F(x) is antiderivative of f(x) , then f(x) is derivative of F(x) .

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Let y = 2x + 3x + 2. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay 2 Submit…

A: We have to find change in y

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: Let f(x, y) = 3x² – x – 3y + 5y2 – 10xy. - - - List the critical point:

A:

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: Suppose f(x,y)=xex. At the point (2,0), in what direction is the directional derivative maximized? |

A:

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point…

A:

Q: xy ,show that: x- y If z = = 0

A:

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

A:

Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

A:

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

A:

Q: 8y If the directional derivative of f(x,y)%D at (2,1) in the direction of (2a,-3) is equal to zero,…

A:

Q: 2. Show that the function u = (xy) + JTY v(y/x) provides the equation y² : 0. dy?

A:

Q: of of and ду Find f(x,y) = Vx + 3y?

A:

Q: Suppose that f(z, y) = e-2-2y –2z+y Then the maximum is

A:

Q: A particle is moved along the x-axis by a force F(x) = x² + 5x – 6 . How much work is done in moving…

A:

Q: Find f, and f,. f(x, y) = 13x In xy

A:

Q: = Let y 2x2 linear approximation + 7x + 4. If Ax = 0.1 at x = to estimate Ay 2, use

A:

Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

A:

Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

A:

Q: The antiderivative of the function 4 .3 + 10x³ is, 4 f(x) - -4 .3 + 2.5x³ + c 4 -10 + 1.0xª + c -4 +…

A: According to question given f(x)=44.3+10x3We have to calculate the antiderivative

Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

A:

Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

A:

Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

A:

Q: which is the best definition of a counterexample

A:

Q: Find fr and fy- f (x, y) = | 5e dt %3| fa(x, y) = fy(x, y) =

A: We apply fundamental theorem of calculas and solve it.

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

A:

Q: Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy. Δy≈ ?

A: y=2x2+7x+4, ∆x=0.3 &amp; x=5 Differentiating with respect to x, we get dydx=22x+71+0=4x+7 Now at…

Q: 2 f(x, y) = x² + 3xy

A:

Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

A:

Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

A:

Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

A:

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.

Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

A:

Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.