2 Ax, y) = V 16 – x – 4y²

Q: Given f(x, y) = x² – 3x?y – y", find fz(r, y) = fy(x, y) = frz(x, y) = fzy(x, y) =|

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Q: Let f(x, y) = 12x² + 7y² + 3x + 3y+ 6 Find D = frz · fy – fåy-

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Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

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Q: Given f(x, y, z) = 2e(z+y), Find fy(0,},-4).

A: here we have to find partial derivative of a function w.r.t. 'y' and here we also use chain rule.

Q: f(x,y)=xe*/2+275x²y³, then at (1,1) is equal to əx²əy³

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Q: Determine the linear approximation of f(x) = x' at x = 1. а. у3 9х +8 O b. Not in the list О с. у--…

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Q: Given f(x, y) = x° + 2xy³ – 2y", find fz(x, y) = fy(x, y) =

A: Given  f(x, y) = x6 + 2xy3 - 2y5.

Q: Let y = x2 – 4.x. With x = 5 and Ax = 1, find the values of Ay and dy. %3D %3D -

A: y=x2-4x , x=5 and ∆x=1

Q: Suppose z is a function of x and y, and csc Vx2 + yz = 2"esin . Solve for dz and ду

A:

Q: If f(x, y) = xy then: V f(1, – 1) =

A: Given function is,  f(x,y)= xy

Q: Q1. Find the linearization of f(x, y)= x² – xy + 12y? +3 at the point (3, 2).

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Q: If Z = x.n. f .f (**²), then show that: X. Zx + y.Zy = y

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Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: If f(x, y) = V + y3, find fy(0, 5).

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Q: Show that the function f(x, y) = (y + ax)?e+ax satisfies the equation given by ах dy?

A: It is partial derivative problem

Q: f) Given w=(x+y)/(z-3y) , Find dw

A: Total derivative

Q: Let f(x, y) = xy+ + 2x²y + 4y5 (a) Find fr- (b) Find fy-

A:

Q: dz Suppose z is a function of z and y, and csc Vr² + yz = 2ªešinz. Solve for dz nd ду

A: Derivate partially wrt x and y respectively

Q: function f(x, y) = 2x^3 + 6xy^2 −3y^3 −150x has four stationary points, find

A: Please refer to the image below

Q: Show that the function f(x, y) = (y + ax)²ev+a satisfies the equation given by %3D a2

A: Please see the explanation below....

Q: Q2) If y(0) = 0 and y'(0) = 0, f(t) = e*", %3D %3D 1 y(t) (D +3)(D + 2)(D + 1)f(t), determine y(t).…

A: Differential equation is a equation that involves an unknown function and its derivative. Ordinary…

Q: Find values of x and y such that both f,(x,y)= 0 and fy (x.y)=D0. f(x.y) =x + xy +y² - 3x+2

A: Given that, the function is fx,y=x2+xy+y2-3x+2. Obtain the value of fxx,y.…

Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

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Q: x2 B) If w = x".f then show that: %3D x. Wx + y. Wy = nw.

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Q: K is between J and L, KJ= 46, and KL = 47. Find JL. Y f(X) Vx X,

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Q: Find the value of n in the function w = x •rn satisfies the equation Wxx + Wyy = 0, where r2 = x² +…

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Q: Find and given f(x, y) = y" In(x²) + - Va 8y

A: Given: Function in x, y is given.          fx,y=y7lnx2+9y3-x47 Objective is to find,…

Q: Q4: Let z = 2x2 – y? . Find all points at which |Vz| = 4. Then find V|Vz| at the point (1,4).

A:

Q: Q1. If g = xy — yz — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F and…

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Q: Let f(x, y) = ax? + by? – 16x + 30y + 14. If the point (2, –5) is the only critical point, find the…

A: Given:      f(x,y) = ax2 + by2 - 16x + 30y + 14      The critical point (2 , -5)    The partial…

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 12. f(x, y) = x² + xy + y² –…

A: We are authorized to solve only 1 question, please repost remaining questions Partial derivative

Q: ,x² y).

A: From the given information, The joint PDF can be expressed as: fx,y={ cx2y ,   x2≤y≤1          = {…

Q: Find fy and f, for f(x, y) = 10(4x – 5y + 11)°. f, (x.y) =O fy(x.y) =|

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Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

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Q: Let f(x, y) = /T²(1 – y²). Find fr (0, 1).

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Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

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Q: Find the absolute maxima and minima of the function f(x,y)= 2x^2-4x+y^2-4y+1 on the closed…

A: See the explanation below

Q: If f(x, y) = xe³y + 4xy, then is given by: dydx 3xe3y + 4 3e3y + 4 xe3y + 4 3 e3y + 4 3

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Q: Find f, and f, for f(x, y) = 11(2x – 6y + 5)*. fx (x.y) =D

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Q: 2. Show that the function u - p(sy) + Vj (y/2) provides the equation 0.

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Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: The x, y, zER, subject to the condition yz + zr + xy = 12. Then greatest value of ryg is (a) 6 %3D…

A:

Q: 1. Given f(t) = 3t2 + 4t - 5 and g(t) = 6t + 1, find: %3D b. g(t)- f(t)

A: Difference of two function g(t)-f(t)=(g-f)t.

Q: Is AX'Y'Z' a reflection of AXYZ across line g? g X. Z' Y X'

A:

Q: Given the function: f(x, y, z) = x²yz + xy+ +1 find: fz(1, 2, 3)

A: We will find fx1,2,3 in the following step.

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.