af af a²f a²f a²f a²f for ду' дх' ду? ' дх?' дхду' дхду f(x, y) = ex²y + xy3

Q: Use linear approximation to estimate (0.99)2 + (3.01)² – (0.99)(3.01). -

A: Topic - approximations

Q: 2. If F = (3x² - 3yz)i + (3y²-3xz)-(32²-3xy find div curl

A: Given problem:-

Q: 3. Find the gradient of U = 4xz² + 3yz. А. 4z3а, + 3za, + (8xz + Зу)а, В. 4z? а, + 3zay + (8xz +…

A: For a vector valued function U≡Ux,y,z, its gradient is defined as gradU=∂U∂xax+∂U∂yay+∂U∂zaz…

Q: Calculate Differentiate. 1 = 2 z² + 1 f(z)

A:

Q: The productivity of a country is given by ​f(x,y)=14.41x0.427y0.573​, where x is the amount of…

A:

Q: (ナ D-)ュ when x= y= 0o,y=y"- I, y CS

A:

Q: d (7) Vtan²s+ 21 dt = dx

A: Explanation of the answer is as follows

Q: Estimate f (2.1, 3.8) assuming that f(2, 4) = 5, fx(2, 4) = 0.3, f y(2, 4) = -0.2

A: Given : f2,4=5.fx2,4=0.3 , fy=2,4-0.2The linear approximation is :Lx,y=f2,4+fx2,4x-2+fy2,4y-4Now,…

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: 4. Calculate(Y/X)- – 2)* if: X = (; -) Y = (% ) z = ( ) (G Đ=z (F- )=« (4- )-

A: We will find out the required value.

Q: Suppose that | f(z)dz = 2, | f(z)dz = 1, %3D [ 9(2)dz = - 5, | 9(2)dz - 2. Then, | (=) – g(2))dz =

A: Given: ∫25fxdx =2, ∫23fxdx =1, ∫25gxdx =-5, ∫23gxdx =-2 To evaluate:∫35fx-gxdx We know that…

Q: x = X, +(-

A: let the initial velocity be v0 , and the initial distance be x0 .and in time t , the new velocity…

Q: Evaluate the integrals

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: 5-4y2 dy 3+2y

A: To evaluate ∫5-4y23+2ydy

Q: Calculate fx (1, 3) and fy (1, 3) for f (x, y) = √(7x + y^2).

A: For a function of two variables, partial derivative with respect to one variable is calculated by…

Q: 2 f(x,у) 3 V9- х* -Зу;B Р(3, - 3); 13 3 13

A:

Q: Find fyæy. .5. .8, f (x, y) = a"y* – 7»®y + x f yry

A:

Q: functions f1(x) = ex+2, f2(x) = ex-3 linearly dependent or linearly independent on (−∞, ∞)? Explain.

A:

Q: Let f(z) = 5z2 + 3z. %3D

A: Given,            f(z)=5z2+3z and         z = 8.2+5.9i

Q: Find fx, fy, fz f(x,y,z) = x – V2y² +z?

A:

Q: f(x) (28z +39)(2r 17)(5z 18)(7z 24) (24 7r)(5z 18)(28z +39)(39r 17) E) da como resultado:

A:

Q: 15. Differentiate using quotient rule: x+2 y = х-2

A: Given, y=(x+2)/(x-2) Then,dy/dx will be

Q: Se-2t if 0 3,

A:

Q: Determine U(Z[x]).

A:

Q: Jzu t>o ニ C <x<L ulx,o)- f(x) -g(x) 4(et)-U,lしt)-。

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: Which of the following gives the domain of

A: We have  fx=x9-x2   Domain: Domain is the set of all inputs for which the function is defined.…

Q: By using false position method find f(x) = e* - 2 u %3D

A: Attached solution :

Q: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

Q: Lt² V4-t² dt V(4-x)/(2\x) x(4-x)

A:

Q: If f(x,y,z) = 3zy²e* , grad f =

A: Here we have to find gradient of given function f(x, y, z).

Q: 8. fz/25 – z² dz

A: Consider the provided integral, ∫z225-z2dz Evaluate the provided integral. Apply the method of…

Q: e^3z analytic or not ?

A:

Q: f(x,y) = VE +

A: Given :     fx , y =t+1t

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: 2. Let f(x) = r³, 0, if reQ if r ER\ {Q} Show that f'(0) = 0.

A: We have given a function ,  fx = x3 , x ∈ ℚ0 , x ∈ ℝ \ ℚ We need to show that , f'0 = 0 We know the…

Q: Determine the concavity of f (x) = x* 6x2 12 x + 2. O a. concave downward (-o, 3) and concave upward…

A: Given,           The function is fx=x3-6x2-12x+2.To find: The concavity of the function.We know…

Q: D.(1,2), where f(x, y) 14x-y in the directionof v (2,-1)

A:

Q: Verify that 0t ду дх дх ду 2. 3 y 3 f (x, у) %3D 2х*у — х"у — ху

A:

Q: az Calcula y z = x4 – 2y3 O 8z 4x3 az -6y? O az 4x – 2y dz = 1* – 6y O dz = 4x3 az = 6y? O 8z 4x –…

A:

Q: af(x,yz) -

A:

Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

A:

Q: dt 2 (t–1)(t²–1)²

A: By using partial fraction we can find the given integral

Q: واجبات اوجد الكل م ما ياني o y = 2t2 + 1, t 5x r2 + 1 y = r = 6x O y = V2u, u = 2Vx

A:

Q: Q4. Calculate div F where F = grad(x' + y³ + z³ - 3xyz).

A:

Q: Use linear approximation to estimate f(3.85) given that f(4) = 5 and f'(4)= 6.

A: Given: - The values, f(4)=5 and f'(4)=6 To estimate: - The value of f(3.85) by using linear…

Q: ų (H)= - 2y, (t) + 24;(4)= Y,(4) - 2y, (t) +2t t 9,lFS +2

A:

Q: Find the domain of the function. 4) f(x) = x2 + 3 A) (-«, -3) u (-3, ∞) C) (-3, «) 4) B) (-*, «) D)…

A: We will find out the required domain.

Q: Find fqix(q|x) for x € {0,1} and all q.

A: Given Information: Q be the continuous random variable with pdf, fQ (q) =6q(1-q)       ; 0≤q≤10…

Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz