Get z = f(x,y), x = es cos t, y= es sin t 2 + əx. 2 2 Show that it's + at. as

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: Q1// B: If u+v=e cos y and u-v=e'sin yfind the Jacobain of the a u, v at (x.y) (1,0) dx,y function

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Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: 8y'' - 12y' + 5y = 6 cos t

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Q: Assume that x and y are both differentiable functions of t and are related by the equation…

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Q: Q2/ find dz ond dZ as function ne U and v if of Z=tan (중), X=u Cos V , 9-u sinV

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Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: Is there a function f(x, y) such that fx : one. If not, explain the reason = e* cos y and fy : = e*…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 2 cos x – sin xy; x = y = 8t t' Enter…

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Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: f(x) cos (at) if t 20 %3D 0 if t<0

A: Given: f(x)=cos αt if t≥0o if t&lt;0

Q: Let v(x, y) cos(4x) sinh(4y). Find f(z)with Im( f(z)) = (x, y).

A: using the concept of cauchy - Riemann equations to find u and putting  the value of u and v (given)…

Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

Q: Express in form y=f(x) by eleminating the parameter x = t , y = tan−1(t3 + et )

A: It is given that,

Q: 2. Evaluate ſ. F · dr where F = (sinx,cosy,xz) and C is described by r(t) = (t³,–t²,t) with 0 < t <…

A: ∫CF→ . dr=∫abF→r→t . r→'t dt     →(1)Now the pieces we need…

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

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Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: SO FO %A4 Find dy/dt. y cos(W10t +1 -sin(ot +11 5. sin(~10t + 11) II + 301 +101 sin(~10t + 11) II +…

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Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: (x,() + x(x, t) = sin(t) u(n, 0) = cos(7), at %3D %3D nER.

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Q: Find dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

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Q: dz at t = dt if z = f(x, y) = x² – 3xy+ 2y², x = x(t) = 3 sin 2t, y = y(t) = 4 cos 2t. Use chain…

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Q: Find F′(x).

A: Given- Fx=∫02xcost4 dt To find- F'x Concept Used- The Leibnitz's theorem as  ddx∫gxhxft…

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Let v(x, y) = cos(4x) sinh(4y). Find f(2)with Im(f(z)) = v(x, y).

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Q: Find the area between the two curves.

A: The area between the curves y=sec2x and y=sin2x on interval 0, π4:The area between curves is the…

Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: Let z = x?y + 3xy+ where x = sin 2t and y dz find = cos t. Use the chain rule to when t = 0. dt

A: See solution below. Using definition of chain rule.

Q: 3. Find dy where; (x+y) =2 o) cos(xy)- 주+ ers + b) e+ u= xlax (use chain rule)

A: We have to find the derivative

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: Assume that z and y are both differentiable functions of t and are related by the equation = cos…

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Q: Vhat is the general solution of (x + y) dx + tan ady O xsinx + cos x + ysinx = C O sinx + y cos a +…

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Q: at and ду ду Suppose that 3x - 4y = t and y =t sin 0. Find dt

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Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

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

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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Q: siven f(x,y,z) = sin (3xy) + 3xyz3. Find fxzy(3,2,2).

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Q: f(t) dt t sin(rx), -? What is the value of f(5) if

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Q: Find f(x)

A: We have to find out

Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: Given f(x,y,z) = 7xyz where x = sin(2t), y = cos(2t) and z = -1t. Find df/dt at t = -1. %3D Give…

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Q: Assume that z and y are both differentiable functions of t and are related by the equation y = cos…

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Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

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Q: 1. Differentiate F(t)= e4t° sin sin 2t [Hint: y = e", u = 4t³ sin 2t.]

A: In this question we have to solve the differentiation of the function.

Q: Find LT for f(t) = sin²(wt), f(t) = cos²(wt) %3D %3D

A: We need to find the Laplace transform of ft=sin2wt and ft=cos2wt Now, before finding the Laplace…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

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Q: F(x, y, z) = (xy — 2², 2x+cos(yz), 2y² - sinz)

A: Given the vector field F⇀x,y,z=xy-z2,2x+cosyz,2y2-sinz . The objective is to find the divergence and…

Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin xz; x = , y=t, z= t'

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