Use the differential of the function f(r, y) = V2r3 + y? to approximate f(1.9, 4.1). . Use the differential of the function f(r, y) = In(r + y³/2) to approximate f(0.1,0.9).

Q: Let y = V7 – x. %3D Find the differential dy when a = 4 and dx 0.3 Find the differential dy when x =…

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Q: Find z = f(x, y) and use the total differential to approximate the quantity. (2.04)2(1 + 8.8)3 −…

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Q: Let y = V7-T. Find the differential dy when r = 4 and dr 0.2 Find the differential dy when r = 4 and…

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Q: find a general sulution to the differential eguatiun using variation of A parametert b)yィyニ tantee…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

Q: Find the function "y" that makes the integral stationary V1+y²y2

A: Please check step 2 for solution

Q: Find the differential of the function f(x,y)=x(e^-y) at (2,0). df=?

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Q: For functionf (x, y) = e*y + cos(x – y), write the first and second order full differentials

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Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y g f(x, y, z) 3D…

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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: Use the differential dy to approximate Ay when x changes from x = 2 to x = 2.04. y = V3x – 2 A. 0.01…

A: Given that: y=3x-2x=2 to x=2.04

Q: Use the differential dy to approximate 4ywhen x changes as indicated. y = V3x – 2; from x = 2 to x =…

A: y= 3x-2Find dy/dx when x changes from x=2 to x= 2.03

Q: Find f(2, 1) and f(2.1, 1.05) and calculate Δz, and use the total differential dz to approximate Δz.…

A: Given

Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

A: Change in y is,

Q: If f(x, y) = 4x? – 8y, then the total differential of f at a = 1 and y = -2 is : O df = 8 dx – 32 dy…

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Q: The differential of the function f(x,t)= e cos(2 tt) at the point (x,t)= (0,1) is given by -2dx +2…

A: Topic- Application of derivatives

Q: Let y = f(x), where %3D 7 f(x) = x + Find the differential of the function. dy =

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Q: Use the differential dz to approximate the change in z = √4 − x2 − y2 as (x, y) moves from the point…

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

A: Formula :

Q: If f(x, y) = 17e* cos x + 6 cot y, then the total differential of ƒ at ( 0, ÷) i : O df = 17 dx + 12…

A: f(x,y)=17e-xcos x +6 cot y

Q: Write the differential dw for the function w = ƒ(x, y, z).

A: Consider the given function w=fx,y,z

Q: Find the differential of the function y= 1/√(u^2+v2), where u and v are differentiable functions of…

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Q: Let y = f(x), where f(x) = 7x5/6 + 5x²/3. Find the differential of the function. dy = X

A: The objective is to find the differential function.

Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

Q: Find the total differential z = 1/2 (ex2+y2− e−x2−y2)

A: The given function is z=12ex2+y2-e-x2-y2. Note that  ∂z∂x=12ex2+y22x-e-x2-y2-2x=xex2+y2-e-x2-y2…

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 and evaluate for the given x and d/x of the function, y = 3x2- x+ 6, x = 2, dx…

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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: Find the differential of each function. (a) y = etan(nt) dy = (b) y = V4 + In(z) dy =

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Q: Let y = f(x), where 3x? f(x) : Зx + 4 ,2 x + 4 Find the differential of the function. dy =

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Q: (a) Find the differential dy. y = V 24 + x2 dy = V 24 +x?

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Q: Q1: Use Green's theorem to evalute S. (xy + y2)dx+ x?dy by the curve y = x and y = x2.

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Q: Find the total differential of  w=x3yz+xy+z+3

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Q: Find the differential of each function. (a) y = etan(rt) dy = (b) y = V2 + In(z) dy =

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Q: Find the differential of the given functions. 1. y= x³ – 2x² + 5 5. y = V1-s2 v2 2. u = %3D v+2

A: In this question, we need to find the differential of the given functions.

Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

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Q: If f(1, y) = 17e cos z+ 9 cot y, then the total differential of f at (0,) is O df = -17 dr + 18 dy O…

A: Given that:-     fx,y=17e-xcosx+9coty  we know that total differential is =     df=fxdx+fydy…

Q: Find the differential of f(x, y) = Væ² +y8 at the point (1, 3). df = Then use the differential to…

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Q: Find z = f(x, y) and use the total differential to approximate the quantity. (2.04)^2(1 + 8.8)^3 −…

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Q: Find the differential of f(x, y) = vx2 + y³ at the point (1,2). df

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Q: Let R(x, y) = Vrỹ = Vx Vỹ. Suppose x is measured as 2 with a possible error in measurement of ±0.08,…

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Q: Find the differential of each f (a) y = 1 + 4s dy =

A: (a) The given function is: y=s1+4s. The quotient rule of differentiation states that d…

Q: Find the differential of the function f(r, y) = ye" at (0,-1). df =

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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: Let W=x*yz.compute the differential dw.

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Q: Find the total differential. w = e7Y cos(4x) + z7 dw

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Q: Find the differential of the function, y = v1+x O 1) dy = Vx+1 O 2) dy = 2vx +1 O 3) dy = %3D 1 O 4)…

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Q: Find differential of the function y = (1+6). dy = dr. When z =5 and dr 0.05, compute the…

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