| Are fi(x) = x and f2(x) = x² orthogonal on [-2, 2] inter- val? Find c and c2 so that f3(x) = x+c1x²+c2x is orthogonal to both fi(x) and f2(x) on the same interval.

Q: is The antiderivative of the function f(x) =. 2x а. 2 In x + c b. 1

A: Givenf(x)=12xAntiderivative of f(x)=?Antiderivative is nothing but integral.

Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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Q: Find constants c1 and c2 such that F(x) = c1xex + c2ex is an antiderivative of f (x) = xex .

A: Given: Fx=c1xex+c2ex is an antiderivative of fx=xex To Find: c1=? and c2=?

Q: Differentiate fx) with respect to g(x) of yx= xsiny

A: To find the derivative

Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: Find the particular antiderivative F(x) of f(x) = x6 1 that satisfies F(1) = 4. - %3D

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

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Q: A function (f) is homogeneous of degree • if and only if : ôf + y = Af (x, y). Does the function…

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Q: 2. Expand the function f(x) = tan-1 x up to the first two non-zero terms in the Taylor's polyno-…

A: Solution is given below:

Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

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

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Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Determine the linear approximation of f(x) = x' at x = 1. О а. уз- 1 х-0 О Б. у3 1x +0 O c. Not in…

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Q: (a) Find the linearization L(x) of f (x) = v25 – x² at a = 3. (b) Use the linear approximation L(x)…

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Q: Find the linearization L(x) of f(x) = cot(x) at x = π/4.

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: The function f : R → R defined by f(x) = cos(x - ) is %3D

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Q: 3. Consider f : R2 → R defined by f(x,y) = y³ + 3x²y – 6x² – 6y? + 2. - (a) Determine the critical…

A: The given function is: f(x,y)=y3+3x2y-6x2-6y2+2

Q: (b) Integrate the function f 1 dx by using substitution and partial fraction. x(2x -1) Hence, show…

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Q: 8. Given for C[0,1] the inner-product function (f,g)=[f(x)g(x)dx , find ||f|| if f(x) = x+1.

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Q: The antiderivative of the function f(x) 4 + 11x is + 5.5z2 + c 4 5.5x + c -4 + 22.0x2 + c -4 +5.5x2…

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Q: Can i get help step by step please

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Q: Write the rational function as a sum of partial fractions: x+1 A B -- A = J.B = + (x-4)(x+7)¯ x-4…

A: Given that, x+1x-4x+7=Ax-4+Bx+7  ----(1) To find A and B, Taking least common divisor on the right…

Q: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: The antiderivative of the function f(z) 0+8 is O8 +1.0z+c -4 0+2.0z+c 8. -4 + 2.0z + c -4 + 2.0z + c…

A: To find the anti-derivative of the given function    Anti-derivative means integration

Q: Find the linearization L(x) of f(x) = cot x at x = 4

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Q: Let f(x)=6x2+1f(x)=6x2+1.Enter an antiderivative of f(x) . . .

A: The given function is,

Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: Find the linearization L(x) of f(x) = cot x at x = 4 %3D -

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Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

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Q: The antiderivative of the function f(r) = 2.5 .0+7.3z is %3D -2.5 + 1.8z +c -2.5 0+1.8z+ c 6. -2.5…

A: We will integrate the function and use c as the constant of integration.

Q: Find the domain of the function f(x,y)=V13032-x + y-> {(x,y) E R2 | y# x2 and ys 13032}. O {(x,y) E…

A: Given, fx, y=13032-x+1y-x2

Q: what is the third-order Taylor polynomial approximation of f(x) = cos(x) around x. = h2/4-1 A h/2-1…

A: G

Q: Suppose f(1) = 0,f(3) = 1,f'(1) = 2 , and f'(3) = -3. Evaluate Sxf"(x) dx. %3D

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Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 3n/2 %3D

A: We have to find the linearization L(x) of the given function.

Q: what is the antiderivative F(x) 0f f(x)=3x^((1)/(2))-x-1that satisfies the condition F(4)=0 A,…

A: Given that:f(x)=3x1/2-x-1, F(4)=0

Q: Consider the function f(x) = 7x° + 9x° – 9 - 9. Enter the antiderivative of f(x) + C

A: T

Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: Find T; (x): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T3(x) = %3D

A: f(x)=cos x at a=0, we have to find Taylor polynomial of degree 5.

Q: Is the function 3Sin26x a special function of the operator d? /dx? ?

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Q: H.W:- Prave.that.he.Maclaurinsevi.of.f(x).=-C0JA 3. (い (2n)! 2 i 5... f.(x)..co3.X.1. メ n=0

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Q: Find the linearization L(x) of f(x) at x = a. f(x) = sin x, a = 0 O L(x) = 3x + 1 O L(x) = 0 O L(x)…

A: L(x) = f(a) + f '(a) (x - a) where, L(x) is the linear approximation of f(x) at x = a. f '(a) is…

Q: The Linear approximation (linearization) of f(x) = at x = 2 is %3D (A) y3D -류(z-1) (B) y = - (x – 2)…

A: Given

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

A: Given that

Q: 17. Find the decomposition of the function h(x)= Vx² - Jx two different ways. %3D

A: