If w = f(x,y,z) = In(x² +y² + z*),x = cost y = sint z = 4VE , then dw -is: 16VE 1-16t Option 3 16 1+16t Option 1 4 1+t Option 2

Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: Find the total differential. w = x7yz9 + sin(yz) dw = 7x°yz° dx + 6.9 7_9 +2 cos (yz) )dy + (9x'yz°…

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Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: Can i get help step by step please

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Q: Let y = 3x + 2x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

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Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: SupposeThat w=XYz+XY +Z+3andx=3cost, %3D Y=35int, z=27, Evaluete dwl dtt= I 2

A: solution.

Q: dy 4. dz at z = - 4 if y = 3x² – 1 and dt Find dt dz dt

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Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

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Q: w dw 16. S w +5 dy 17. S 25 - у2 18. S(2x) (x – 1)* dx

A: According to our company's guidelines I can only answer first three subparts of the question since…

Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: d?z dz +3- 2z = te-2t dt z(0) = 0 ; z'(0) = -2 dt2

A: Given differential equation is, 2 z'' + 3z' - 2z = te-2t z(0) = 0; z'(0) = -2

Q: Let y 5x + 6x + 2. If Ax = 0.2 at x = 1, use linear approximation to estimate AY Ay =

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Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

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Q: If x2 + y? + z2 = 9, dt dy = 9, find dt dz when (x, y, z) = (2, 2, 1). = 4, and %3D dt %3D

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Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

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Q: dw If w = f(x,y,z) = In(x² +y² z?),x = cost y= sin t ,z = 4VE , then is : dt + ww.

A: Given  w = f(x,y,z) = ln(x2 + y2 + z2) x = cos(t) , y = sin(t) and z = 4t Substituting the values of…

Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: Assume that x = x(t) and y = y = y(t). Let y=x^2+4 and dx/dt =2 when x=5. Find dy/dt when x=5

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Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: 2. y(2x – y + 1)dx – x(3x – 4y + 3)dy = 0

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Q: Let y=2x^2+3x+3. If Δx=0.1 at x=4, use linear approximation to estimate Δy Δy≈

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Q: In Exercises 28-34, find ƒx , ƒy , and ƒz .

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Q: 1, use 2x2 + 3x + 2. If Ax linear approximation to estimate Ay Let y 0.4 at x = Ay 2

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Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

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Q: Suppose w = x³yz + xy +z+3 and x = 3 cost, y = 3 sint, z = 2t. Then dw dt t= . [Show solution.] =

A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

Q: Find the linear approximation to h(x) = Vx at x = 2. Use the linear approximation t approximate the…

A: Introduction: The linear approximation of a function at a given point is an application of…

Q: Let y = 5x + 3x + 4. If Ax = 0.1 at x = 5, use linear approximation to estimate Ay Ay =

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Q: Let y 3x + 4x + 4. If Ax = 0.4 at x = 1, use linear approximation to estimate Ay Ay =

A: Given, y=f(x)=3x2+4x+4 ,∆x=0.4 at x=1 Differentiate with respect to x, we get f'(x)=6x+4 At point…

Q: 16. Let y = 4x² + 7x + 4. If Ax = 0.2 at x = 2, use linear approximation to estimate 4y Ay 2

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Q: Integrate  zex^2 + y^2  over the cylinder  x2 + y2 ≤ 25, 2 ≤ z ≤ 5.

A: Integrate zex^2 + y^2 over the cylinder x2 + y2 ≤ 25, 2 ≤ z ≤ 5 as follows.Here, x2 + y2 = 25 and…

Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: dy at z = 5 if y = 5x² + 4 and dt dz Find 3. dt dy dt

A: Given y=5x2+4 -1and dxdt=3

Q: If x2 + y2 + z² = 9, xp 6, and dy = 9, find dt dz when (x, y, z) = (2, 2, 1). dt dt dz dt

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Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

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Q: * If z = f (x, y); then its total differential can be expressed as дz dydz date - ( 7 ), v + ( ;) -…

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Q: - By using integration by parts method, calculate the following (choose TWO only) 1- , 2x e* dx 2-…

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Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

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Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

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Q: Let y = 4a2 + 8x + 2. If Aæ 0.4 at x = 5, use linear approximation to estimate Ay %3D %3D Ay =

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Q: sech 2t dt Evaluate 3, coth 2t

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: 2. Reverse the order of integration of S Saz dxdy. y+2

A: The objective is to reverse the order of integration