Complete the table. y = f(g(x)) u = g(x) y = f(u) y = (6x – 2)4 U = y = u4

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 fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

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Q: 3 y=-3 x=- √√9-y² V25– x – y’ dxdy=

A: The given problem is to evaluate the given double integral in Cartesian coordinates. We have to…

Q: y" + 2y' +y = e-*

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: v² =v² +2a(s-s) i. j. K = = kx² 2 k. T = 27 е g ,a = ,X = ,g =

A: This question can be solved using the concept of explicit function.

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Q: 12x the axis, x n bounded by the curves = x2 +4

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Q: (D³ + 4D² + 9D + 10)y - 24 e*; when x = 0, y = 0, y' = -4, y" = 10. %3D

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Q: determine L−1[F].

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Q: 2.F Find y" given y = (x² – 3x)(x* + 5). %3D

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Q: y'' - 6y' + 9y = x^-2(e^3x) using Methods of Variation of Parameters

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Q: 3. Is the function y = Cx² a solution to the ODE y" – xy' + y = 0?

A: Solution is given as below:

Q: "+y=と(t - kT), y(0) = 0, / (0) = 1. k=1

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Q: XI. 6 F dF where F = (x³ – y, x + e') and C is triangle with vertices (0,0), (3,0), (4,2).

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Q: Q Find the domain of y 1- Vx + V+ 3x-x – 3

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Q: Eo f is y = 1(a- 4). 3D1

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Q: I'+yz² -2xyz = f(x*y+y*z+z*x)

A: Given:- x3+yz2-2xyz=fx4y+y4z+z4x

Q: 11t? Given - 17t -3 6 1 t3 - 3t2 t - 3 (11t2-17t - 3 dt = Evaluate (Don't forget to include the…

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Q: | d²y +y³ = 0 dx² is not linear. صواب İhi

A: True

Q: 9. T: R² → R², T(x, y) = (x + 2y, y – x) 10 T. D2

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Q: f(x) %3D e 3.

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Q: fx,y (x, y) = Evaluate E[Y]X = 0.8] > given by [(x + y²), 0 < y ≤ 1,0 < x≤1 0, otherwise

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Q: df-1 For the function y = f(x)=x²-x-1, x ≥ 0.5, find dy (ƒ-¹) '(1) = y=

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Q: e(12)x+ c2e' (5/2)x ans: y=cje 1. 4y"-12y'+5y=0

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Q: df-1| For the function y = f(x) = x + 3x + 1, > 1.5, find dy (f-)'(3) = %3D

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Q: y" + 4y' + 3y = 15 e^2x + e^-x

A: Given differential equation is: y''+4y'+3y=15e2x+e-x Solution of differential equation is sum of…

Q: 2. (D² + 8D + 16)y = 1-e4x

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Q: Letters F &amp; G

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Q: S Ve3x dx A 2 X- e3 2. C + C ez* + C - 1 e3x + C 3. + C - 3. 23 B

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Q: y" - y' - 2y= e* %3D

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Q: %3D 42. Find f(x) dx for each graph of y = f(x). (a) y. (b) y 2. 1. 3 aronh of flr) = 2x + 3 and

A: Given query is to find the valuebof intgy from the graph.

Q: 5.) y = x3 + 1, y = 0, x = 1 around the a axis.

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Q: d²y 2. Determine of the function y = dx2 x²cos (x)

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Q: [v= -y +2x ,x' = 4y + x + t

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Q: Find the linearization L (x, y) of the function f (x, y) = V101 – 4x2 – 9y? at (-2,-3). L (x, y) =…

A: In the question it is asked to linearize the function f(x, y)= 101-4x2-9y2 at (-2.-3).

Q: a.f(x, y) = (x² +x + 1)e¬r²/10-y²

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Q: Approximate y(2.1) using the points (2,0.693147) , (2.1,0.741937), (2.2,0.788457), (2.3,0.832909),…

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Q: Find the function​ y(x) satisfying d3y/dx3=36, y′′(0)=14, y′(0)=5, and y(0)=8.

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Q: Find dy. 3 y = x³ (15-47) dy = (Simplify your answer.)

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Q: dF h(x) = x² + 5x – 1, g(-8) = 3, g'(-8) = –9, and F(x) = g(x)h(x). Find %3D dx

A: We know, ddx[u(x)v(x)]=v(x)ddx[u(x)]+u(x)ddx[v(x)]

Q: 3x The y, of y''-6y'+9y = by using variation of parameters is: .A Y,(x) = -In(x). e 3x 3x -e |

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Q: Consider the function y= g(I)= -z² + 3c + 6,

A: The derivative of the function f(x) with respect to x is given as .

Q: f(x) = e² ; 0 5) = %3D

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Q: e3x-y+z (e*)³e² ey True False

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Q: (c) f(z) = -I Vr E |-1,.

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Q: f (x, y) x+ 3 ху 3 Бъ-х

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Q: S(3x².fu)+x°, f'(x) dx =24 so, so, f(2) = ) %3D

A: We have to solve the given question. Derivative of the function f(x) can be written as f'(x) Product…

Q: (D² – 4)y = 2 – 8x; when x = 0, y = 0, y' = 5. %3D ANS. y = e2x – e-2* + 2x – }.

A: We have to find solution of given differential equation.

Q: Q3) Find fog(x), gof(x), D, D fog' gof x+2e f(x) = » g(x) = vx – 2 %3D 2

A: Solution:-