S:P1 P, defined by S(a + bx) = (-4a + b) + 2ax and T:P → P, defined by T(a + bx) = b/2 + (a + 2b)x

Q: Q4. Find the values of the constants a, b, c so that - F = (axy + bz³)ī+ (3x² − cz)j + (3xz² − y)k…

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Q: Find the nullity of T.T: R4→R2, rank(T) = 2

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Q: To convert the nonlinear DE xy²y' = y³ – x³ to become a linear DE we use the substitution y= u"…

A: Given the nonlinear DE  xy2y' = y3-x3

Q: Use the chain rule to find where First the pieces: End result (in terms of just t): = 历 内 z = x²y +…

A: Here given that                       z=x2y+xy2,  x=3-t3,  y=3-t6 We have to find dzdt by using…

Q: Given that y,(x) = e<* is a solution of y" - y' - 2y = 0, use the Reduction of Order formula to find…

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Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

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Q: Given that y' = 2x2 – y + 3y2, where y = 0.5 at x = 2. Estimate the values of y(2.2) using the…

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Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: Q1. Find the linearization of f(x, y)= x² – xy + 12y? +3 at the point (3, 2).

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: Find a general solution to the DE (D^2 + D - 6) y = 5e^2t by using the Reduction of order

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Q: ди Use the Chain Rule to find for x + Y и — y + z when x = p+ 5r + 9t, y = p– 5r + 9t , and z = p+…

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Q: Q:2: a) Find implicitly, if y²cosy +x² = 2xy

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Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: 4) Suppose that T : R³ → R² is defined by T((x, y, z)) = (1+2x – z , 3 – x + 6y) Is T linear?…

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Q: dw ,s = 1 If w = 2x? ds + y, x = 2 - s, y = 1+ 2s², then by chain rule when %3D సా | 8

A: See the attachment

Q: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a have a…

A: Given: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a…

Q: Find a general solution to the DE (D^2 + D – 6) y = 5e^2t by using the Reduction of order

A: If you have any doubts in the solution please ask me  in comments i will reply you as soon as…

Q: Given F(r, s, t) = r(3s² + 3t²), compute: Frst

A: Solution of question is written in below steps.

Q: Let z = 9xy - 9x y where x = 6t, y = 8(1 - 1). Find by using the chain rule. Express your answer in…

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Q: A second solution y2 for the DE x²y" – 4xy' + 6y = 0, can be obtained by reduction of order with the…

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Q: ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

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Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: Use the IVT to show that e−x2 = x has a solution on (0, 1).

A: Given equation is

Q: A second solution y2 for the DE x²y" – 4xy' + 6y = 0, can be obtained by reduction of order with the…

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Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

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Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: EX. Evaluate the JJ(X*+2xy+y") dydx when step size of x = 0-2 and step Size of y=o.5?

A: Given: ∫01∫02x2+2xy+y2dydx with a step size of x=0.2 and y=0.5.

Q: Find the solution of the PDE t> 0, x = [0, π] x= [0, π] √u₁-ux = U₂ [u(x,0) = 3 senx + sen3x,

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: dz Let z = Vx2 + y?, x = s2 - t2, and y = 2st. Find az and at using the Chain Rule. as

A: Given, z=x2+y2, x=s2-t2  and y=2st

Q: Use the chain rule to find the value of 4 when t= 1. dt z = 2x2 – 2y, x = 2 + 2, y = 6t – 6

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Q: Find the value of x and KL if K is between J and L. JK = 2x, KL=x+2, and JL = 5x - 10.

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Q: Let z = (y - 2x) ³, where x = s′ s²t and y = st². Use the Chain Rule to dz find when s = 2 and t =…

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Q: Let 2 = (y - 2x) ³, where x = s²t and y = st². Use the Chain Rule to find when s = 2 and t = -1. Əz…

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Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: z=f(x,y)=x^4-3xy+1 and x=2t, y=t^3 find dzdt using the chain rule

A: Given query is to find the derivative using chain rule.

Q: The general soslution of x' = x + 2y and y' = -3x -4y is given by: a) x = 2c1e-t + c2e-2t, y =…

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Q: 11 f(x,y) 3x-7y+2, R is the rectangle with opposite car- ners (-1,0) and (1,3).

A: 12. Given: fx,y=2x+2y+2 and triangle with corner 0,0 To find the area of the triangle. The formula…

Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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Q: (a) The function z depends on u and v so that z = 2v(4- 3u)? u = 2x + 3y and v= 3x-2y az when x 0…

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Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: Let z = √√√7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2. ds

A: To find out the given partial derivative.