Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate f(-1.99,0.01). %3D 10x2 b) z = ; at (4, – 1) and use it to approximate f(4.01, –0.9). x-y'

Q: Find the differential dy for the given values of x and Δ x. y = 5x 2 - 2x + 3 ;  x = 2 , Δ x = - 1…

A: Given that: y=5x2-2x+3,  x=2  ,  Δx=-16

Q: Find the linear approximation to the equation f(x, y) = 5 ln (x* – y) at the point (1,0,0), and use…

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (- 0.01) xe…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y dy

A: use chain rule while differentiating

Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 5 y%3D 2x - 5 dy =

A: Given:y=x+52x-5Differentiation formula:ddxxn=n.xn-1ddxuv=vdudx-udvdxv2

Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: Find the differential dy of the given function. (Use "dx" for dx.) y%3D 2x . -5 dy

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Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: Use the differential dy to approximate Ay when x changes as indicated. y = V3x – 2; from x = 2 to x…

A: Topic - approximation Using derivatives

Q: Find the differential dy, then evaluate: y= 2x3+ 6x-| when x= -2, dx= 0.l

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Given: y=ln9-x2 To find the differential dy

Q: dw Use the Chain Rule to find where w = cos 12x sin 4y, x = - dt and y = t". 4 dw

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Q: Let y = v6 – x. %3D Find the differential dy when x = 1 and dx 0.1 Find the differential dy when x =…

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Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

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

Q: Find the differential dy of the given function. (Use "dx" for d> y = 8x² – 4 dy = %3D

A: Formula :

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: Find the linear approximation to the equation f(r, y) = 4 ln(z – y) at the point (2,15,0), and use…

A: Given: fx,y=4lnx4-y We have to find the linear approximation in two variables.

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: Find the differential of the function f(x, y) = 3xe2y at the point (5, 3) using Ar = 0.25 and Ay = (…

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Q: Find the differential dy of the function y = Provide your answer below: dy = dx 5x4 + 4 4x + 3

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Q: The equation implicitly defines z as a function of t. Find dz dt 11 dt cos (3 z) = -8

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Q: Let y = tan(4r + 8). Find the differential dy when a = 3 and dæ = 0.1 Find the differential dy when…

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Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: Q4) Use the chain rule to express dy /dx in terms of x and y y = sin t and t = cos x where t = 0

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

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Q: Find the differential of the function. 3 z = 3t - t2 dz II

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Q: Let y = 4 a. Find the change in y, Ay when x = 3 and A¤ = 0.3 %3D Find the differential dy when x =…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: Find the differential of the function. z = e-5x cos(9xt) dz = dx + dt

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Q: Find dw/dt using the appropriate Chain Rule. Function w = x sin y x = et, y = π - t dw dt || Value t…

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Q: dv dv 5. Use the Chain Rule to find and ds v = ln (2.x + 3y), where x = s sin t, y =t cos s %3D

A: Here, Givenv=ln(2x+3y)∂v∂x=22x+3y∂v∂y=32x+3yAlso, x=s sin(t)∂x∂s=sin(t)∂x∂t=s cos(t)y=t…

Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

Q: se the Chain Rule to find dw/dt. w = INVX2 + y2 + z² x = 9 sin(t

A: Here we have to use the chain rule to find dwdt=? w=lnx2+y2+z2, x=9sin(t), y=3cos(t), z=5tan(t)

Q: Use the differential dy to approximate Ay when x changes as indicated. y = V3x – 2; from x = 2 to x…

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Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Linear measurement is one-dimensional. A linear differential equation is an equation where the…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: Find the differential of the function. Z = e-9x cos(2rt) dz = dx + dt %3D

A: The total differential of the function  is given by . So, to find , first we need to find the…

Q: Find the differential dy of the given function. sec² x y x² + 2 sec 2x (2x²tan x + 4 tan x-2x)…

A: This question is based on quotient rule

Q: Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Given  data  xey+2z-cos(xy)+ey-ln2=4  ,  A(ln2,0) Also given  when x changes by (dx=0.01) and y…

Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

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Q: Find the differential of the function f(x, y) = 4x2 + 9xy + 8y at the point ( - 3, 1) using Ax = -…

A: To find - Find the differential of the function fx, y = 4x2 + 9xy + 8y2 at the point -3, 1 using ∆x…

Q: Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3

A: In this question,w is function of x,y,z and x,y,z are the function of t so first we find out…

Q: Find the differential of the function f(x, y) Ay = 0.05 . - 8x y at the point (4, 5) using Ar = -…

A: Given; The given differential function fx,y=-8xy at the point (4,5) using ∆x=-0.3  and ∆y=0.05

Q: Use the Chain Rule to find dz/dt. z = sin(x) cos(y),    x = The Square Root of t,    y = 8/t

A: Given: z = sin(x) cos(y),    x = √t,    y = 8/t By Chain Rule,

Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5

Q: Let y=(x2+4)to the 4th power. Find the differential dy when x=3 and dx=0.3.... Find the…

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Q: Let y = 3a?. Find the change in y, Ay when x = 1 and Ax = 0.3 Find the differential dy when x = 1…

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