f is a function of only x, g is a function of only y, and f and g satisfy ln(f(x)) + ln(g(y)) = ln(1 + x + y + xy), find f(x) and g(y).

Q: - (4y" + fy) = -A with y(-1) = -2, y(-1) = 1, y"(-1) = 0 Use x1 = y, x2 = y', and x3 = y". x + with…

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Q: Find constants c1 and c2 such that F(x) = c1x sin x + c2 cos x is an antiderivative of f (x) = x cos…

A: To find constant c1 and c2 such that Fx=c1 xsinx+c2cosx is an antiderivative of fx=x cosx. Solution:…

Q: f(x) = sin 2x,x e [0,2n]

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Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

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

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Q: The critical point of the function* f(x, y) = x² + 5y² + 2 cos x

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Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: z = x3 – xy? + 3y2

A: Let us consider the two variable function z=f(x,y) The first partial derivative of the function is…

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: Find the value of a so that the function f(x) = xe has a critical %3D point at x = =D3. NOTE: Enter…

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Q: 1. Find the critical points of the function 2 f(x, y) = x² + 4xy.

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

Q: 2. z = x + 2 У Х x

A: Solution

Q: Find the absolute maximum and absolute minimum values of f(x) = x ln ,e). on

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Q: Show that the function f(x) = e1/2)[(x-µ)/a}° has a relative maximum at x = µ.

A: fx=e-12x-μσ2 Differentiating with respect to x, we get…

Q: 4. Find and classify the critical points of each of the function f(x,y) = x² + y² + 3xy.

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Q: et f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

A: Let f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: Find the most general antiderivative of the functions: 1)f(X)= 2secxtanx-3sinx 2)f(X)=…

A: (1) Given, f(x) = 2secxtanx-3sinx  ∫f(x)dx = ∫(2secxtanx-3sinx )dx               = ∫(2secxtanx)dx -…

Q: Find the antiderivative of f(x). f(x) = 3e6x+ sec2(x) +x3

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Q: The derivative of y= (V x - 2 )(Vx+1) is equal to: х - 1 A 2x+1/x-2 2х-1 B Jx+1/x=2 2х-2 2/x+1/x-2 D…

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Q: Find the linearization L(x) of the function f(x)=x^3/4 at x=1

A: Given, f(x)= x³/4 x=1 Therefore, f(x=1)=1³/4 f(x=1)=1/4

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: Find the Linearization L(x) of y= (3+ x)-1/2 at a = 1. L(x) =

A: To find the Linearization.

Q: Find and classify all critical points of each of the function: a.f (x, y) = (x² +x + 1)e¬²/10-y² f…

A: Solution is given below:

Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

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Q: Show that (0,0) is a critical point of f(x,y) = x kxy + y2 no matter what value the constant k has

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Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Given a function y² z f(w, x, y, z) = 2(w + 1)²x - xe² + W which of the following is not part of the…

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Q: Find the critical point/s of the function f(x,y) x³+2xy-2x-4y

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Q: x² +y² F(x,y) = is a homogeneous function of degree x- y

A: We have to find the degree of the homogeneous function

Q: (b) Find all first and second partial derivatives of z = x² In(x² + xy).

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: (b) Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x? + 3y + 3x + 3xy +…

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Q: Find the linearization L(x) of the function at a. f(x) = Va, a = -8 L(x) =

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Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

A:

Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: Find the linearization L(x) of the function at a. f(x) = e5x a = 0 L(x) 1 + 5x %3D %3D

A: We have to find linearisation

Q: Show that the linearization of f(x) = (1 + x)k at x = 0 is L(x) = 1+ kx.

A: We need a linear approximation formula for f(x).

Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: Find the critical point (x0,y0) of the function f(x,y)=(√(x2+y2))+1.

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Q: 4) Let g(x,y) = 2x² + y² – x²y. a. Find the critical point(s) of g. b. Use the second derivative…

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Q: Let y : R → R be the real-valued function defined on the real line, which is the solution of the…

A: The differential equation is given as Y’  = -xy + x , y(o) = 2 From the type of the problem we can…

Q: Find ý of the function x2 - e2x+3y - In(xy) = 0. %3D

A: Consider x2-e2x+3y-ln(xy3)=0We differentiate it implicity, we…

Q: Find constants c1 and c2 such that F(x) = c1xe -x + c2e -x is an antiderivative of f(x) = 3xe -x .

A: Given: Fx=C1xe-x+C2e-x  and fx=3xe-x

Q: Find constants a and b in the function f(x) = axb such that f(-) = 1 and the function has a In(x)…

A: Given that the function is  f(x) = abx/ln(x) such that f(1/2) = 1 and the function has a local…

Q: 2) z³ - 3x ²y + 6 xyz = 0; use the method of partial differentiation Əz Əz to find 2x 1 ду

A: The given equation is z3-3x2y+6xyz=0. Find the differentiation ∂z∂x, ∂z∂y of the given equation.…

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: Find the linearization L(x) of the function at a. f(x) = e5x, a = 0 %3D L(x) 1 + 5x

A: f(x)=e5x point a=0

Q: Calculate the derivatives of all orders: f'(x), f"(x), f"'(x), f(4)(x), f(x) = e3x - 1 f(x) = 3e3r-1…

A: We use chain rule to find these derivatives