30. Find an equation for the tangent plane to z = f(x, y) at (3, -2) if the differential at (3, -2) is df = 5dx + d y and f(3, -2) = 8.

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: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18…

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Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

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Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: Prove that if the family of integral curves of the differential equation is cut by the line x = k,…

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Q: A firm has the Cobb-Douglas production function y = 10x}^^x!7²x}^. Currently, it is using the input…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1 olve for the differential of y when y = sinxx, x=-, and dx=-. 2 3 A 2 В 4 C 2 D 4

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Q: 3. Is the expression (ez+y+z +4x²y²2²)dx+(e²+y+z +r’yz²)dy+(e²+y+z+³y²z)dz = 0 %3D exact? If yes,…

A: Given expression is ex+y+z+4x2y2z2dx+ex+y+z+83x3yz2dy+ex+y+z+83x3y2zdz=0 To verify whether the above…

Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: y" + 4y = cos(t−3) +4t, y(3) = 0 _y (3) = 7

A: Solution :

Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .…

A: Given equation is

Q: 11. Find the length of the curve x = on the interval [2, 4] (integrate with respect to y) 12y3

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Q: Obtain the differential equation of all straight lines at a fixed distance p from the origin * O…

A: The general form of equation of a line which is at a constant distance c from the origin is…

Q: x² (y + z) – 4V/x²+ y² + z² = 0,

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Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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Q: Find the differential dy. x + 3 4x - 1 dy =

A: y=x+34x-1

Q: Let 2x2+ 3x+Y a) Find the differential dy when x = 1 and dx=0.1 %3D b) Find the difiea ial dy when…

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Q: fy = f(r), how do we define the differential dy

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Q: Find the differential of the function z=2x'y %3D

A: If z is a function of two variables defined by z=f(x,y) then the differential dz or total…

Q: 6. If f( x, y) = V x° + 1 y², estimate the value of f( 2.06 , 4.97 ) using the differentials.

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Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

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Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

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Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: Compute the differential dy for y = 7x° – 4x2. dy =||

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Q: Suppose y = (x² + 5)³. (a) Find the differential: dy dx. (b) Compute the differential when x dx 2…

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Q: Compute dy/dx at P=(2,1) on the curve y^2x^3 + y^3x^4 - 10x + y = 5

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Q: Compute the differential dz of the function. z = a°!l 9,,11 dz

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Q: dy 4. y dx ;y(1) = 3 x(х+1)

A: In this question , Firstly we can integrate on both sides and solve the integral. After that we can…

Q: Find the equation of the two lines that are tangent to the curve x 2 + 4y 2 − 4x − 8y + 3 = 0 at…

A: Given

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ ( 1. (D³ - 5D² + 3D + 9)y = 0 2. (D³ - D² –…

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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: 1. Use the differential df to approximate the change in the value of f(x,y) from the point (1,0) to…

A: We will be using definition.

Q: The Soluton Curve for a differential equartion of the form an-y= 3n, passes through dy + passes. the…

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Q: Express x = ln(7t), y = 9-t in the form y = f(x) by eliminating the parameter.

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Q: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D

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Q: Let y=3x^2  Find the change in y, Δy when x=5 and Δx=0.1    Find the differential dy when x=5 and…

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Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).

Q: Find the differential dy. x + 2 y = 9x - 1 dy =

A: In this question we have to find we have differentiation of y.

Q: Explain, the given differential 3x²dx + 2yz dy + y² dz is exact or not.

A: We will check whether  3x^2dx+2yzdy+y^2dz is exact or not.

Q: Compute the differential dz of the function. 6.7 Z = x dz ||

A: Here, to find the differential dz of the function z=x6y7 Note that: dz=zxdx+zydy...(1)

Q: Let y = 3x² + 8x + 3. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when…

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Q: Solve the differential equatic y' = (x + y + 2)², Chart Area y(0) = 2 by setting u = x + y + 2.

A: y'=x+y+22let u=x+y+2     u'=1+y'     y'=u'-1

Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as:

Q: Calculate the increment and differential of the function y=x2−x+1 at the point x=2 when dx=1.

A: Given, the function is y = x2 -x +1 at the point x = 2 and dx = 1, We have to calculate the…