Consider the function f (z) = e2: (b) Show that if f (z)is purely imaginary, 2n + 1 then z = п %3D 0, +1, +2, ... 4

Q: The gradient of the function 2x1 + x2 - 3 evaluated in x = (0 0 0) is: OA. Vf=(1 2 3)T OB. Vf=(0 0…

A: Solution:

Q: 2. Show that the function u = p(xy) + Vry (y/x) provides the equation y². 0. dy?

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Q: Find linearization of the function f(x) = Vx + 3 at a = 1 and use it to approximate V3.98

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Q: dy from t dx n for y as a function of x, and find two results are consistent by expressing the (a)…

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Q: Find the linearization of f(x, y) = V1+x - y? at (4, 1), and then use it o approximate f(3.96,…

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Q: hich z ∈ C the function e^(1/z) is holomorphic?

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Q: Evaluate f fs 2² dS, where S is the portion of x2 + y² + z² = 2 in octant 1.

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Q: Find the linear approximation of f(x) = e(a) at a = 1.

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Q: | f(t) dt = x*e* e + a

A: This question is based on integration.

Q: c) Find the second degree polynomial approximation to f at (a, b) = (1, – 2) T2(x, y)

A: Given :- The second degree polynomial approximation to f at a,b = 1,-2 f x,y = -x2y2x2 +y2

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

A:

Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: 2. Find frxz for f(x, y,z)= z² e³xy

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Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 25 L(x) =

A: The solution of the problem is given in the next step.

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 the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ] 3

A: Solution: The objective is to find the linear approximation

Q: For the function f(x, y) = (cos x)ey +v 1 + x + y. %3D Show the process of using the linearization…

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Q: In Exercises 3–8, compute f'(a) in two ways, using Eq. (1) and Eq. (2).

A: Given

Q: d) The function +(xy)-r*r2y) exp G 18xy is homogencous in of degree X and

A: The given function is: f(x,y)=(x2+2y)e2xy+8xy...(1) The function f(x,y) is said to be homogeneous…

Q: Find the linearization of the function given below at the specified p f(x) = 4 In(x) at a = 1 L(x) =…

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Q: Find the function f(x) and all values of c such that

A: To find the function f(x) and all values of c such that∫cxf(t)dt=x2+x-2

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

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

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Q: Compute the convolution f(t) * g(t) for f(t) = e-3, g(t) = 2t.

A:

Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

Q: Find the linearization L(æ) of the function at a. f(z) = V7, a = -8 L(x)

A: We can find the linearization as below.

Q: a) Find the linearization of the function f (x) = Vx at a = 9. %3D %3D b) Use part a) to approximate…

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Q: Consider the function f(x) = 2æ³ – 6x² + 8x – 9. An antiderivative of f(x) is F(x)= Aæ4 – Bæ³ + Cx²…

A: The given function is : f(x)=2x3-6x2+8x-9         The antiderivative of fx is the value of integral…

Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

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

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Q: Give an example of a linear function f(x)= mx + b, with m,b ±0 and an interval a<xsc where f(x)dx=0…

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Q: express the given function f in the form f(z)=u(x,y)+iv(x,y) f(z)=(ez^2)

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Q: Find the linear approximation of f(x) = Vx +I at a = 1.

A:

Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: Find the linear approximation of f(x) = Vx at xo = 27.

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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: In Exercises 3–8, compute f'(a) in two ways, using Eq. (1) and Eq. (2).

A: Given function is fx=1x. To evaluate f'a at a=2. Power rule of differentiation states that:…

Q: Consider the function z = f(x,y). If fx(a,b) and fy (a, b) both exist, and they are equal, then the…

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Q: e of the function g(x y, z) = 1/xz + e%.

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

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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 the local linear approximation of the function f(x) = V1 + x at xo = 3, and use it to…

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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: b) Let X₁, X₂, Xn-f(x) = {0x-(0*) x>1 e. w. find Suff. Comp. St.

A: Given that

Q: Find the linearization L(x) of the function at a. f(x) = Vx, a = 16

A: