y P = (x1, y1) Ут ly2 – yıl У2' P2 = (x2, y2) |x2 – x|| X1 X2

Q: Find the partial derivatives fx (3,5) fy (3,5) for the function f(x,y)= y^2/x-y

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Q: One of the critical points of the function z = f(x,y) = 4x -12xy+ y +1 is (0,0,1). [Notice that I !!…

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Q: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: Find f(-1,1,0) f(x,y,z)=(2xy-y^2+z)/(x^2+3xy+z)

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Q: Classify all the critical point(s) of f(x, y) = 22 + 6x? – 3y3 – 150.x. Find maximum and minimum…

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Q: Examine for minimum and maximum values of f(x,y,z)=2xyz-4xz-2yz+x^2+y^2+z^2-2x-4y+4z

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Q: v² dx + x(xt y) dx = 0 LINE 1 let x= v2, dx = yda+ zdy y2 (ydz + zdv) + xz(vz +Y)dy= 0 vz (vdz t…

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Q: Solve ux – uy +yu = 0, where u is a function of x and y. %3D

A: Given: ux-uy+yu=0. The objective is to solve u, where u is a function of x and y.

Q: yUx-xUy=U , U(x,1)=2+e^-x

A: Given partial differential equation is, yux-xuy=u      .....1. With initial condition ux,1=2+e-x.…

Q: Find the values of x, y and z that correspond to the critical point of the function: z = f(x, y) =…

A: We will find the first order partial derivatives and equate them to 0 to solve for the critical…

Q: Find the total differentials for: y=−5t3 − 12tz − 6z5 y = (5t2 + 7z)(2t − 4z3)

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Q: If f(x, y, z) = 12ry - 2yz - 6zx + 7, then the first order partial derivative f = O - (2y – 6x) (2y…

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Q: 3 (D² + 4)y = Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{v} = T+4 + F(2+4) 3 3e 3s 1le-3s s(s² +4)…

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Q: Vx2 +1 – Vx² – 1 y = Vx² +1+ vx² – 1 2.x3 dy = 2x - d.x - - show that Vx4 – 1 -

A: Given: y=x2+1-x2-1x2+1+x2-1      ......(1) To Prove:  dydx=2x-2x3x4-1      ......(2)

Q: 2. Locate the critical points and identify which critical points are stationary points: (i)f(x) =…

A: 2 Given: f(x)=4x4-16x2+17 To find critical points first we will find derivative of this function and…

Q: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

Q: Find the values of x, y and z that correspond to the critical point of the function: f(r, y) = 5x² +…

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Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: Find both first partial derivatives. ху f(x, y) x² + y2 f,(x, y) = f,(x, y) =

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Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) 2x2 +…

A: Given: z=f(x,y)=2x2+8x+5y+5y2-10xy Finding, dzdx and dzdy So,…

Q: 2. y = V4-x , x=0 and y=0 about the y- axis

A: Given that y=4-x2, x=0 and y=0 about the y-axis

Q: Find L(y). y +2x = 2 Y – x' = et y (0) = x (0) = 0 %3D %3D -2 L (y) = %3D s(s²+2) 1 O L(y) = (s2+1)…

A: Given; y'+2x=2 y-x'=et y(0)=x(0)=0.

Q: derivative

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Q: Identify the transacation of point P x + 3, y + 1). ddf2d92a ddf892d342a ddf892d342a dd1892d342a…

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Q: 7) Let Z.= 3x2 - y² . Find all points at which |VZ| = 6 %3D

A: There is an ellipse,  all points on the ellipse are the solutions of given equation.

Q: Find the rate of change of f (x, y, z) = 3xyz in the direction normal to the surface yx² + xy² + yz²…

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Q: x² + y² = (2x² + 2y² – x)', (0,¿), (cardioid) -

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Q: dz for the function z = 20y² x Find the partial derivative dz 20y /x ду dz = 10y /x dz = 40y /x dz =…

A: We have to find

Q: (3z²+5z+3)dz (z- 2)(z+3) Integrate:

A: The given integral is ∫(3x2+5x+3)(x-2)(x+3)2dx

Q: Find the orthogonal trajectories of x^2+y^2−2cy=0

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Q: find the first and second derivatives. 1. y = -x2 + 3                                2. y = x2 + x +…

A: 1) Given thaty = -x2 + 3On differentiating y with respect to x,

Q: Find L(y) y" - y = 1 0st< 2 It+1 t2 2 y(0) = y'(0) = 0 °L (1) = + +] -2s e %3| s(s2-1) s2-1 -2s L…

A: The given differential equation is: y''-y=1         0≤t&lt;2t+1t≥2;…

Q: At what interval is y=2x4- 4x2 concave downward? Ux> 3 3 3 3 V3 3 <x< 3 3 <x< V

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Q: X~N(3, var=9), Y=7X-6, find pdf of Y

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Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 3x? -…

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Q: hich vect וdtiolו y and 2? 1 -2 y = 1 -6 x = 2 8 -1 2 -1 5 2 -3 [ 2 -1

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Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: etermine whetter fie differential eguetion is linegr or non lineqY and Ne reasons-

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Q: Classify all critical points for f (r, y) = 2x2 – y3 – 2ry.

A: Disclaimer: Since you have posted multiple question, we will be answering only first question for…

Q: 1 y" – 2y' + 2y y(4) = 0, 3 (4) = 0. -

A: Given: The given differential equation is y''-2y'+2y=1x, y4=0,y'4=0

Q: Find the four second partial derivatives. z = 6x2 + y5 a2z дхду дудх ду?

A: We will find all the asked second order partial derivatives as following.

Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: dN1 =rN1 dt (1-*) - aN1 N2(1 – exp[-bN1]), K %3D dN2 = -dN2+ N2e(1 – exp[-bN1]), dt

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Q: 3. Find general Golution y" + y= Secx

A: Given that, find the general solution y''+y=sec3x (D2 +1)y=sec3x

Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4

Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: Find both first partial derivatives. f(x, y) = 3x - 9y + 8 F,(x, y) f,lx, y) = |

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.