[x, y]²=[-1,0]=-1

Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: Give the general solution to the equation x' Ax where A = %3D

A: To find the general solution of the given system, first we find the eigenvalues and corresponding…

Q: from y = ae + be %3D 2.

A: y=ae4x+be-4x ....(1) Differentiate both side w.r.t x dydx=4ae4x-be-4x        ....(2) From (1) and…

Q: 2. y"-y-6y = u(t – 1) – u(t – 4); y(0) = 1, y(0) = -1

A:

Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: 2. F(x, у) %3D — (у i-2x) y2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: If y2 is positive, then y1 + y2 will lie _______ y1 by a distance equal to ____.

A: Consider a function y=sinx+1. Here y1=sinx and y2=1>0positive.

Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

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Q: Verify that ƒxy = ƒyx, for ƒ(x, y) = 2x3 + 3y2 + 1.

A: To verify that

Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: B. Find the first and second derivatives of i- y =-10x+3cosx+(2x+3)(5x-4x) 5x+1 ii- y= 2x

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Q: f(x, y) = 1 + x2 - y2 R = {(x, y): x2 + y2 < 1}

A: Find the area of surface given by z= f(x,y) that lies above the region R.

Q: t(s² + t?)ds – s(s² – t²)dt = 0 %3D -

A: We have,  ts2+t2ds-ss2-t2dt=0 On re-arranging and solving a bit furthermore, we get the result as…

Q: y'(t) = In(y- 3) %3D

A:

Q: Find x and y in terms of a. X + y = 0 х+ ay %3D 6 (а + 1) (х, у) —

A: Given:    x + y =0        --------1   x + ay = 6     --------2 from 1: x = -y put the value of x in…

Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: Solve Xy"-xy' +y = a+3ln(x), y)=Q , yl)=1 %3D

A:

Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: The local linear approximation of (1- x)2° at x, = 0 is a) 20 - x c) 20 +x b) 1- 20x d) 1+ 20x

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: f(z, 9) = 82" + 5y² + 4z°y+ e7=y of Calculate

A:

Q: find dy/dx

A: Known formula: ddx∫rxqxftdt=fqx q'x-frx r'x.

Q: how can i find the vectorial equation for d1:3x/2=y-1 and d2:?x+y-6=0

A: Given: vector equation for  L1:   3x/2=y-1 l2  :   x+y-6=0

Q: y"-2y'+y = e* Inx

A:

Q: х2у" + x(x-1)у' + (1-x)у %3D 0

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Q: Find dy2 of z = 2x – 5xy² + x² y° %3D -

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Q: Find: 군x, 군y, Zxx , 군ys, 군xy, 2sx = X+y Xy-1 Z =

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Q: x, prove that y¨= 2(y² +1)(3y² +1).

A:

Q: Solve for x, y z from X - 1 1 2 Z 3. 6 6

A: 2x-113y=2z66

Q: Find (x, y): R = {(x, y): 0 ≤ y ≤ √√x² +1,0 ≤ x ≤ 1} about the x-axis.

A:

Q: Evaluate the Cauchy principal value of 2x² - 1 fo dx. x4 + 5x² + 4

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Q: y'+2y/x=x, y(1)=2, y(2) using h=0.1

A: given :y'+2yx=xy(1)=2, y(2) using h=0.1

Q: fy = e*, y = 1 - e-x, and x = 0 ab- %3D

A: Given: - The curves of, y=e-x, y=1-e-x and x=0 about y=4.5 To find: - The volume of a solid is…

Q: Solve for the orthogonal tragectories y²= 4x (1- kx) %3D

A: This question is based on differential equation.

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: the functiOn y sin 2-x+ -2, deter

A: Amplitude, period, phase shift and vertical shift: A periodic function is of the form…

Q: x, y) Edy is

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Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: - 6х + 2у, dt dy -3х + 1у dt

A:

Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: Express (2xy + 2x – 1) – (x² – y² – 2y)i in terms of z & z, then simplify. - -

A:

Q: f(z) = (x²+y)+i(y²-x) is analytic %3D

A: We have, fz=x2+y+iy2-x Compare the equation with fz=u+iv we will get u=x2+y and v=y2-x Now,…

Q: Solve Utt - c²uxx = 0, –n 0, %3D и(х, 0) %3D f(x), и(-п,t) %3D0 %3D и(п,t), и,(-п,t) %3D 0 %3Du,…

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Q: f (x, y) x+ 3 ху 3 Бъ-х

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Q: y" = 2x – 3, y(0) = 1, y(1) = 1,0 < x < 1 %3D -

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Q: Find fxy(x,y) if f(x,y)= e 4xy². fxy(x,y)=

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Q: Find the orthogonal trajectories of x2 + y? – 2cy = 0

A: