dw 22. If w = f(ax + by), show that b = 0. a ду Hint: Let ax + by = z.

Q: Let f(z, y) = zy-y+a?. D.((1,2) =? where u=. OA- O B. -37 Oc- 37 OD.

A:

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If a² + y} = 29, %3D and d = 1 when a =…

A: The given equation is x2+y2=29. Now find the derivative dydt, when x=5, y=2 and dxdt=1as follows.

Q: Let y = [f(u) + 3x]^2 and u = x^3− 2x. If f(4) = 6 and dy/dx = 18 when x = 2, find f ’(4).

A: Given y=f(u)+3x2Differentiating with respect to x  dydx=ddxf(u)+3x2

Q: Let F(t) = * F(e)dt (dont include the «C) Fine Question Help: D Video Add Work

A: We know, ∫tndt=tn+1n+1 ∫-sin-tdt=∫ddt-cos-t=-cos(-t)

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2.…

A:

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: If f(æ) = S Tm dt for x > 1, 1 | In t find f'(2).

A: Please refer the attached image for complete solution.

Q: State fuo oer femnme egual JF.T ds gimn fow line into f.T ds givern that

A: In this question we have to find two other form of line integral.

Q: QO use best linear approximation to (F(Xiy) = ²³ to estimate the value of f at the point (0.0),…

A:

Q: If f(x, y) = xsiny + e" , then V f(x, y) = (0, e'). Select one: True OFalse

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Use the linear approximation of f(x) = /2x - 3 about c = 2 to estimate the value of V1.32 Enter your…

A: Given that: f(x)=2x-3

Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

A:

Q: now if we take F (x, y) = (ax, ay), where a is any positive constan %3D

A:

Q: Let f (x, y) = 9e2xy what is fryx (x,y) =? %3D

A:

Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

A:

Q: Let A = {x E Z: 8x} and let B={rEZ:12lx}. Then * ACB ВСА None of these A=B

A:

Q: Suppose that the only Införmation we have ab8ut a fuRcEiOH FIS y= f'(x) (a) Use a linear…

A: Given: f(1)=-7

Q: dz 2 = -ry", where r = st“ and y = –st". Compute – as a function of s and t only evaluate this when…

A:

Q: Let f(x,y) = ax + by2 af where a and b are constants. If of at x = 1 and %3D ху y 2, then the…

A: Introduction :

Q: Let flt.v) = y+3r²e!. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

A:

Q: Let f: R -----> R be defined by: Vx ER, 3 ifx #2, fr ifx =2' Then: as x -> 2, fx -> 3. Show: Vɛ > 0,…

A:

Q: It is always the case that f(x, y) dydx = f(x, y) dædy. OTrue False

A:

Q: dx Show that f - In|ax + b| + C where a # 0. ax+b

A:

Q: If f(x, y) = 8xey + 8y Inx, then is given by:

A:

Q: 24. If f(x, y)=x²y+cosy+ ysinx, find fu, fyy & fry.

A:

Q: Let f(z) = kz5 + az + cz. Find v(x,y) if z = 6.3 + 3.3i, a = 8, c = 12, andk = 5. Round off vour…

A:

Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: 10. If z = x + f(u), where u = xy, show that дz dz х дх = x. ду

A:

Q: Find Sea)ax Jf(x)dx if = 56 foR X<to (x fok xZ6 flx): %3D

A:

Q: 2. Let f(x,y)=xe" and find a) fx, fyr fy

A:

Q: (c) Show that |(−1,1)| = |R|, where (−1, 1) = {x € R : −1 < x < 1}.

A:

Q: If f(2) = | * t3 dt then f'(x) = and f'(6) %3D Submit Question

A:

Q: 10.Show that F(x, y) = (1 + xy)e*yi + (ev + x?e*y)j is conservative and find a function "f" such…

A:

Q: Q9. If W = f(u)=u' + sinu+Inu, and a=ax+by, where a, and b are constants, show that aw aw b. ax

A: We have to prove the given statement.

Q: Q3. If F = x'a, + y'a, + (z² – 1) a̟, find F· dS, where S is defined by r= 2, 0 < z < 2,0 < ¢ < 2r.

A:

Q: O show thet fu) =2a +3b is Candin Uous where a, b are Constants.

A:

Q: If f(x,v) = (y)²x ,Verify fy=fx ху

A: Given:fx,y=y2x Now, the value of fxy will be,fxy=∂2f∂y∂x=∂∂y∂f∂x=∂∂y∂y2x∂x Now, the value of ∂y2x∂x…

Q: Suppose Vf(x, y, z) = 2xyzexi + zex¯j + yex k. If f(0, 0, 0) = 1, find f(1, 3, 3). ,2 .2

A:

Q: Suppose Vf(x, y, z) = 2xyze*i + ze*j + ye* k. If f(0, 0, 0) = 1, find f(3, 1, 3).

A: follow next step

Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

A:

Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: 6) Show that TE[f (t - a)] = e-i2mva TF[f(t)] where a e R".

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

Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

A:

Q: . If z = f (x, y), where x = e" - e and y = e - e", show that TM UT az x: az az az dy ax UTM UTM UTM…

A:

Q: Q4 * If f(z) = z? ;z = x + iy Show me u(x, y) ;v(x, y) Determine ux; Vy|

A:

Q: 2. If f(x, y) is a function of y only, then S" S fdxdy Si fdy. %3D

A: Given query is to find statement is true or false.

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.