h(x) = Vx – 2 on the domain [2, 5]. -

Q: Let  f(x, y) = sin(15x2 + 3y2) Calculate the quadratic approximation of f at the point (0,0)

A: Given that,  fx, y=sin15x2+3y2 The quadratic approximation of the function fx, y at the point x0, y0…

Q: Find the linearization of x+1 f(x) = 2 – dt 1 + t“ at x = 1.

A: Given function is

Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

A:

Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

A:

Q: Find the linearization at x = a. IT f(x) = sin³ (x), a = 4

A: Given,            The linearization at x=a.             fx=sin3x, a=π4We know that,             The…

Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

A:

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Find the derivatie: F (+2 %3D (-t*+*z+)た =人

A:

Q: Find the absolute maximum and minimum of the function f (x , y) =x² + y² on a closed triangular…

A:

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find the best linear approximation to f(x) = x² on the interval [0, 2].

A: Here we use Taylor's approximation.

Q: Obtain the orthogonal trajectories of xy = C and compute for the positive value of y at the point…

A: Solution

Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

A:

Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

A:

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

A:

Q: of of and ду Find f(x,y) = Vx + 3y?

A:

Q: Find the critical point of the function f(x, y) = 1 - x – 6x² – 8y + 3y?

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Q: Find the linearization of f(x) = 3+ S" sec(t - 1)dt at .2 END x = -1

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 3. Evaluate f 2xdx + (y + 2)dy along the rectangle with vertices (0, 0), (0,3), (3,3) and (0, 3).

A:

Q: Find the linearization L(x)of the function at a .

A:

Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

A:

Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

A:

Q: Find and classify the critical points of f(x,y) = 4r+20² - y²

A: Find and classify the critical points of f(x,y)= 4x+2x2-xy2.

Q: What does it mean for the differentiability of a function if the Cauchy-Reimann equations (Ux = Vy…

A:

Q: 4. F(x) = (1- t) dt %3D 4

A:

Q: Find the linearization of the function f (x) = x³ at x = 1. L(x) = Using this linearlization, ƒ…

A: Answer is in next step.

Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

A:

Q: Find the linearization of ƒ(x) = √1 + x at x = 0

A: Consider the following function: fx=1+x Differentiate fx with respect to x: ddxfx=ddx1+xf'x=121+x

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

Q: Suppose that f(x, y) = e¯4z² - ly + 7z + 2y then find the discriminant of f.

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Q: Q, Frd the donain of H fallowing function: fa) = 5x -3x-4

A:

Q: Q.8 Find the gradient Vw ofthe function w = In /x² + y² + z². %3D

A: Given function W=ln(√(x2+y2+z2)) Now we will find the gradient as shown below

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

A:

Q: - Given f(x, y, z) = x In(yz³), find fzy and fyz.

A:

Q: Find the linearization L(x) of the function at a. f(x)= sin(x), a= π\4

A:

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: 2 f(x, y) = x² + 3xy

A:

Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

A:

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 the 2nd solution using reduction of order. xy" +y' = 0; y1 = Inx For the toolbar, press ALT+F10…

A: Just I have used the method of reduction of order and solve in detail and find that  Second solution…

Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

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: Estimate v16.3 using the linearization L(x) of f(x) = /x at a = 16. (Use decimal notation. Give your…

A:

Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.