[E] (i) Define the term linear combination.

Q: əz Use chain rule to find z = x² + 3wxy + w², with x = 2t + 1, y = et and w = 3 – t2.

A: The aim is to find, The formula for chain rule is,

Q: Given functions sin3x and 2sin3x are a. Linearly Dependent b. Linearly Independent c. Both are…

A: The two functions f(x) and g(x) are linearly dependent if and only if one function can be written as…

Q: (c) Compute of using the Chain Rule. of дf дх дf ду дf dz. + дя дх дя ду дя дz дя (Use symbolic…

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Q: Express ax? + bx + c as a linear combination of the functions f(x) = 4, g(x) 2x, and h(x) = -x²,…

A: Sincewe can write every element of P2 in linear combination of f(x),g(x),h(x) so this functions…

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x3 - 2x + 3, a = 2

A: We find f(x) and f'(x) at x=2

Q: Given f (x) = x³+ 5, let L(x) be the linearization based at 2. Find L(2)

A: Given,          The function is fx=x3+5 and the linearization based at 2.

Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: 6. Use the Chain rule to determine fs, an f(x, Y, z) =

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Q: Determine if the ODE (1+ x*)y' + y = e² is linear or not. O linear O nonlinear

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Q: Find the linearization of ƒ(x, y) = x2 - xy + 1/2 y2 + 3 at the point (3, 2).

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Q: Find the linearization L(x) at x= a. f(x) = x+ a = - 1

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Q: Let f (x, y) = (x − y)e^x . Use the Chain Rule to calculate ∂f/∂u and ∂f/∂v (in terms of u and v),…

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Q: Q-2 Show that the functions f(x) = x and g(x) = |x| are linearly independent when considered as…

A: Linearly dependence: Two functions f and g are said to be linearly dependent if there exists a…

Q: Find the linearization of ƒ(x) = 2/(1 - x) + √(1 + x) - 3.1 at x = 0.

A: Here The formula for the linearization is Here a = 0 Therefore,

Q: F(2) = (2t – 1)° dt using the Fundamental Theorem of Calculus.

A:

Q: Are the functions fi (x) = e+6 and f2(x) = e-7 linearly dependent or independent?

A: In this question, we have to check two given functions are linearly dependent or independent.

Q: Check whether the function f(2) = e5² satisfies the Cauchy-Reimann equations or not.

A: 2) The given function is f(z)=e5z. Check whether the function f(z)=e5z satisfies the Cauchy-Riemann…

Q: Find the MRSxy of the utility function U=In(x)+y.

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Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: [2] Show that the functions f (x) = 4x" , and f,(x) = x*+* linearly independent (-00, 00). are on

A: To Show: Show that the functions f1x = 4xn, and f2x = xn+4 are linearly independent on -∞, ∞…

Q: Find the Linearization L(x) of y = (1+x)¬1/² at a = 8. L(x) = %3D

A:

Q: find the linearization L(x) of ƒ(x) at x = a.ƒ(x) = sqrt(x2 + 9), a = -4

A: Given function is, fx=x2+9, a=-4.   The objective is to linearize Lx of fx at x=a.   It is known…

Q: d evaluate r(g(1)) using the Chain Rule. dt r(t) = (e' , e21 , 4), g(1) = 4t +9

A: Given that rt=et, e2t, 4 and gt=4t+9 We have to find ddtrgt using chain rule.   The chain rule is…

Q: Find the covariance between x and y

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Q: Use the chain-rule and find x and y in terms of x, x, and if:

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Q: Find the linearization L(x) at x = a. 1 f(x) = - x - a = 1 %3D -

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Q: Differentiate the following using the Chain Rule: 1.h(x)=( 3x-2)*

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: Can i get help step by step please

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Q: Find the linearization L(æ) of y = (81+ 2æ²)-1/2 at a = 0. L(x) =|

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Q: Determine if the functions Y1=e^{4x}senx and Y2=e^{4x}cosx are linearly independent or linearly…

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Q: B. Differentiate the following using Chain Rule. 3.f (2) = (322- 플 + z)" (3=² – +=

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Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

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

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Q: 1. Use the Chain Rule to find y = (u-2)³ and u = da in terms of x. 1 2x+1

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Q: Je and ди dv Je (in terms of u and v), using the following chain rule formulae: evaluate

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Q: Find the linearization L(x) of the function at a. f(æ) = VT, a = -8 L(x) = %3D

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Q: Find the linearization of ƒ(x) = 2/(1 - x) + saqrt(1 + x) - 3.1 at x = 0

A: Given,

Q: say f(3)=5, f'(3)=-2 and let g(x) =xf(x/2) find the linearization of g(x) at x=6

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Q: Use the generalized chain rule Question Let f (x, y, z) = 2x² + yz, x = /t, y = t² , and z = ÷. Find…

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Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = 3√x, a = -8

A: Given function is fx=x3 Linearization of function is given as: Lx=fa+f'ax-a At a=-8 f-8=-83=-2…

Q: Find the value of x so that the following are linearly dependent in R³. (1, –1,0), (-1, x, 0), (0,2,…

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Q: Let r (t)= - The x component of r' (-1) =

A: r'(t)=<2t,3,5> r'(-1)=<-2,3,5>

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x + 1/x, a = 1

A: Given fx=x+1x

Q: Given f (x) = x³+3, let L(x) be the linearization based at 4. Find L(4)

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Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

Q: Determine whether the following are linear operatorson Rn×n. L (A) = 2A

A: