Show that f(a) = 1€L2[0,1] but g(z) = r L2 [0, 1]. %3D

Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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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: compute for antiderivatives f(x)= x2-2 f(x) = x(x-4) f(x) = 3x2+2x+1

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Q: Find an upper bound for ||L|| where L: R² → R³ with L(x, y) = (2x + y,x + 3y, 3x – 2y) -

A: Here we use the definition of boundedness of a linear operator.

Q: If F(x)=sinx+6x2−4 is an antiderivative of f(x) then f(x)=

A: If F(x) is antiderivative of f(x) , then f(x) is derivative of F(x) .

Q: 9/ Verify that Way Wxy = Wyx %3D W = e +X Ln y +g Ln X

A: Given that : W=ex+x.lny+y.lnx Do derivative w.r.t 'x' , we get : Wx=ex+lny+yx Now, do the derivative…

Q: Suppose that F(x) = –3x* is an antiderivative of f (x) and G(x) = 2x' is an antiderivative of g(x).…

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Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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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: xsin-1(x) is 1– x² If x =0.58 and y = 0.31, then value of C in the antiderivative of F(x) = %3D %3D…

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

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

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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: What must be true of F(x) and G(x) if both are antiderivatives of ƒ(x)?

A: For a function f(x) to be anti-derivative of F(x), f'(x) should be equal to F(x).Similarly, for g(x)…

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: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Consider the function f(x) = 3z10 + 3z° – 3z² – 4. Enter the general antiderivative of f(z)

A: Given function is : f(x)=3x10+3x5-3x2-4 We have to find antiderivative(integral) of the given…

Q: 교꾸가고 (a, y) + (0,0) (x, y) = (0,0) f(x, y) = x2+y2 is discontinuous at (0,0).

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Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: Let A = {(x,y) = RXR; 0<max{|x-3], ly- 2|}<1}, then: *

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Q: Find the general antiderivative of f(x) 3 – 4x* + - 5VT x3 Preview 2.

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

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Q: if the function u= ln (x^3+x^2y-y^3/x-y) then x su/sx + y su/sy is

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Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

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

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Q: Let f (x, y, z) = ln(x2 + z) + y2 exz. Find fzyx

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Q: If f(x) = 1-x* , then an antiderivative F(x) could be Inx| -x А. 6-x C. 5x 3x 5 Inx| – x* 1+x° В. D.…

A: f(x) = 1-x5xAntiderivative F(x) = ∫ 1-x5xdx∫ 1-x5xdx= ∫1x-x4dx= ∫1xdx - ∫x4dx= ln x - x55 +…

Q: 2. Find the most general antiderivative of f(x) = 3+22 %3D

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Q: lim, f(x)= 0, then | f(x)dx diverges

A: Statement:  limx→∞ f(x)≠0,  then ∫1∞ f(x) dx   diverges.

Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: b) Use the chain rule for partial derivative to find 2 when z = f(x, y) = x²y + ln(x + y) and (x, y)…

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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 linearization of f(x)=1−∫3x+124/(3+t)dt at x=2.   upper limit of integral = x+1 lower…

A: Linearization

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: Let = f(x,y) = x² -y. Use Euler's method ( with step size h = 1) to approximate the value of y(2) if…

A: The Euler method is a first-order numerical procedure for solving ordinary differential equations…

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: Consider the functions f(x, y) = x2 − y2 and g(x, y) = x2 + y2 .                             (a)…

A: Given functions are f(x,y)=x2-y2  and g(x,y)=x2+y2.

Q: [4xy + 2x] 5) Let F(x, y) =[ 2x² + 1 Is F conservative? If so, give a potential function for F. %3D

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find fzyx If f (x, y, z) = ln(x2 + z) + y2exz

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Q: a²y azy C2 for 0 0 %3D at2 y(0,t) = y(L,t) = 0 For t > 0 For 0sxs5 y(x, 0) = f(x) = L L - x For <xSL

A: In this question, we solve the boundary value problem δ2yδt2=c2δ2yδx2the B.C:…

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: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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

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