4. Assuming that the equation F(U, X1, X2,..., xn) = 0 implicitly defines a utility func- tian U = f(x1, x2, ..., Xn) : (0) Find the expressions for , aU/axn, ... %3D pand ax4/axn.

Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

Q: 1. Find the orthogonal trajectories of the family of curves x? + y2 = cy.

A:

Q: Then, the only positive equilibrium point of Eq.(1.1) is given by (2.7) (1 – A) (E Bi) Li=1 provided…

A: Given linearized equation of Eq(1.1) about y~ takes the form ;…

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A:

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

A:

Q: Show that the function z = f (x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: 2. If f (x) = Sn* et? 0, dt, find f'(x) V2t+sect

A: The solution is given as

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A:

Q: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A: To find - Determine the orthogonal trajectories of the family of electric field lines described by…

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

A:

Q: 5. If c is a critical point of F(x), when the is a local maximum or minimum at c? Explain

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Q: 7. what is the durivative oF q= arc cSc V1-3X %3D 3 Cz -Gx)I- 7 X 3. C2-6x)1-3x (-3x)-3x 3 C1- 3x)-3

A: First make it in simple trigonometric functions then diffrenciate it and just put all the given…

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A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: 8. Find the extremum and saddle points of the function f(x, y) – x3 – 3xy + y3 if any.

A:

Q: 11. Find the linear approximation to given function at indicated point (Баллов: 2) x2 z = 3 + +, Po…

A: Topic:- linear approximation

Q: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

A: Due to Bartleby guidelines, only 1st question can be answered if multiple questions have been asked.…

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Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2

A: Since you have posted multiple question in this question so I have solved first question as per our…

Q: 2. Find the critical points of f(x, y) = x³ + y³ – 3x? – 3y + 10 and classify each of them as a…

A:

Q: 2. Show that the function u = p(xy) + Vry ý(y/x) provides the equation n, = 0. dy? U -

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Q: 18. Use the Linear Approximation to f(x, y) = /x/y at (9,4) to estimate 19.1/3.9.

A:

Q: For the function f(x,y)=x^2+x−3xy+y^3−5, does the critical point (1/4,1/2) correspond to a local…

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Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

Q: 5(a) Determine the orthogonal trajectories of the family of electric field lines described by the…

A:

Q: Which conditions make (a, b) a critical point (stationary point) of f(x,y)? What does the sign of…

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A: Given : f(x, y) = 1 - x⁴ - y⁴

Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

A:

Q: If y(t) solves the IVP dy = y2021 y2019 y(2021)= -2019, dt then lim y(t) is: t- 00 Oa. 1 O b. 00 O.O…

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Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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Q: Suppose fn → f and the functions fn all satisfy the Lipschit condition |fn(x) – fn(y)| < Mx – y| for…

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Q: 1 Justify the Cauchy-Riemann equations for f(2) = e² where f(z) is holomorphic.

A:

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: 3. Determine if (х — 1)2, if x 1 is differentiable at x = 1.

A: Given  hx=x-12if x≤1x-1if x&gt;1

Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: Show that the function z = f(x,y) = x³ – 3x² – 4y² + 2 has one saddle point and one maximum point.…

A: Given a function in two variablesz=fx,y=x3-3x2-4y2+2

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

A:

Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

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Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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Q: 1. Explain how would you determine the maximum value of y= 1 3-cos x

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Q: Find the value of k that makes function continuous at z=4 |2z + 6 z> 4 5z – k z< 4 f(z) = ualuo…

A: Continuity.

Q: = 1 Find the minimum value of f(x, y, z) = 3x − y − 3z subject to x² + 2z² - - and x + y -z = 0.

A: