ди and ди ди Q3. If u = e"" sin p, p= sin x, q = z' In y, r=1/z, use chain rule to find

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Q: Find div F and curl F if F(r, y, z) = 10e i- 2 cos yj+ sin2 zk. %3D

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Q: let y= (x + sin(x)) Find gix), fcx) e deriv ative f(x) = so that y=(fog)(compute usin Chain Rule ニ

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Q: If f(x,y,z)=e3x+4ycos5z  then satisfy laplace equation

A: Given function is: fx,y,z=e3x+4ycos5z The condition for Laplace equation is: fxx+fyy+fzz=0 Partial…

Q: aw If w = (x+y + z)2, x = r-s, y = cos(r + s), z = sin(r + s) then where r = 1, s = -1 ar using…

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Q: ikt 三 ik ik Ikt. ik こ

A: So we have to solve the inverse Fourier transform to get the expression for U(x,t)

Q: 2. Using first shifting property, find the Laplace Transforms of: (te sin(at))ª when. a = 1

A: Solution:Given  tetsinataSubstitute a =1Let f(t) = tetsinat

Q: Q3. If u = e'' sin'p, p=sinx, q=z²Iny, r=1/z, use chain rule to find ди ди > ах ду , and ди

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Q: dz and du dz Use the Chain Rule to find when u = 1 and v = -2. dv z = In q, q = v + 3 arctan u

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Q: 3) roțațion 90° counterclockwise about the origin

A: We know that,  90° counterclockwise rotation: (x,y) becomes        (-y,x)

Q: Solve using Fourier analysis U=U + 4 cos(2x), u(0,t) = 0, u(r, t) = 0, u(x, 0) = sin(3x) + cos(2x).…

A: Using separation of variables and Fourier series expansion.

Q: a. Using Laplace transformation evaluate sintx x(1+x²) dx

A: Given the expression ∫0∞ sin txx1+x2 dx we have to use Laplace transformation to evaluate.

Q: (a). u(x, y) = e- sin y, (b). v(x, y) : = cos x cosh y, %3D

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Q: U(x, t) = 4,(x, t), 00 u,(0, t) = 0, u,(1, t) = 0, u(x,0) = cos 2mx, 4, (x,0) = -2m cOs TX %3D

A: In this question, we solve the boundary value problem by using the method of variable seperation…

Q: dz and du dz Use an appropriate form of the chain rule to find dv z = -; x = 14 cos u, y = 17 sin v…

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Q: 3. u, = u, - sin x cos t, 1 >0 В.С.: и(0, г) %3D0, = () 1.С.: «(х, 0) %3D 0, u,(x. 0) = 0

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Q: Fis)-S-65-15 -359

A: Solution is given below:

Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: (a) x, = a+bZ, +cZ,- • (b) x, = Z, cos(ct)+Z-1 sin(ct). (c) x, = Z,Z, •

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Q: a) u=r³-3ry² + 2xy + x, D) u= x² - y² +5, c) a= sinh rsing, d) u = e(y cos y + x siny), e)…

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Q: OSolve where y (0, t) = 0 = y (5, t) and y (x, 0) = 10 sin 4Tt x.

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Q: Find and using the chain rule, if uw = In(x² + y*), x = e" sin(u), and y = e" cos(u). w%3D

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Q: QI by the chain rule iplakdy 订 =(sin x)cox x = sin-ly+ cos(er) %3D and Find dy

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Q: x+y then x +y- ôy If u= cos %3D +.

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Q: y, 4e* In y, x = In (u cos v), y = u sin v; 4e* In (u, v) = (2, π/4) 7. z =

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Q: əz Use chain rule to find at where z = e2" sin (30) and r = st – t², 0 = Vs² + t². %3D

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Q: Use an appropriate form of the chain rule to find and if z = xe" , x = 2uv , ди y = sin(uv). You…

A: By using the definition of  chain rule for two independent variables we find the value of ∂z∂u, and…

Q: when u = 0, v =1 if du Use Chain Rule to find z = sin ry + x sin y, r= u² + v² and y= uv.

A: Given: z=sinxy+xsiny, x=u2+v2 and y=uv. To find: ∂z∂u at u=0, v=1. Solution: Partial derivative of a…

Q: How do I solve the laplace(u(t-2)cos(t-2))

A: The Laplace transform formula for translation on the t-axis is given by ℒ{u(t-a) f(t-a)} = e-asF(s),…

Q: az az and du #6. Use the Chain Rule to determine given that av z = x sin (y? – x) x = 3u – v?, y =…

A: Solution:-

Q: de dx -KA- = Qgiven that 0(0) = 0₁ and 0(t) = 02 then show that = 0₂-01 t -KA-

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Q: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use…

A: From the given data: t = x4 y9 x = S cos (t) y = S sin (t)  dt = d (S cos (t)4 (S sin (t))9…

Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

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Q: 3. 2.m (ris, t)= e cos (25) y= h(ris, t)- e sini (s) %3D + そ人メ+ (てん「以) =1 け! ne Use chain rule to…

A: Given, u=fx,y,z=x3+xyz+z2x=gr,s,t=e2rcossy=hr,s,t=e2rsinsz=mr,s,t=ercos2s To find: ∂u∂s Formulas…

Q: dz and du dz Use an appropriate form of the chain rule to find dv z = =; x = 16 cos u, y = 13 sin v…

A: In this question we have to find differentiation with respect to u and v.

Q: If f(z) : f'(z) =D %3D coS I - 6 tan z, then %3D

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Show that z- sinh z Rcs :* sinh z

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Q: The Jacobian of the transformation ac=r cos 0, y =r sin 0 is r. Select one:

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Q: Base on the graph, make a conjecture about whether the circulation and flux of F = (r, - y) on %3D…

A: Given:  F→=x,−y,C:r→t=3cost,3sint for 0≤t≤5π6 a:To compute the circulation and interpret the answer,…

Q: Let z = x? – x*y where x =r sin 0 and y = r cos 0. əz əz Use the chain rule to find and ar - Give…

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Q: Find div F and curl F if F(x, y, z) = 4º®Y¡ – cos yj+ sin² z k. - div F= curl F=

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Q: az and ди az Given that z = exy, x = 2u + v, y = , find (using chain dv rule).

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Q: Laplace inverse of L-1 is 6! 5!

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Q: 5] Sketch the graph of r(t) direction of increasing t. (sin t, 2 cos t) and show the %3D

A: Given: r(t) = (sint, 2cost)

Q: Use the Chain Rule to find zz and zy given sin(u) tan(v), u = 3x + y, and v = x – y. %3D

A: Given z = sin(u) tan(v)where u = 3x + yv = x - y

Q: x(t) = e-al, a> 0. %3D

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

Q: Use the Chain Rule to find az/as and az/at. (Enter your answer only in terms of s and t.) z = sin(0)…

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Q: dz and du dz Use an appropriate form of the chain rule to find dv z = -; x = 14 cos u, y = 13 sin v…

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Q: Laplace inverse of L is |(8 – 4)2 + 6² e ot sin 4t O ebt sin 4t O et sin 6t O e 4t gin 6t

A: L-16s-42+36 Apply inverse transform rule: if L-1fs=ft then L-1Fs-a=eatft Noe for 6s-42+36⇒ a=4,…