3+ 6x 5x + 12 Find x if BC = and XC = %3D 10

Q: xydy – (y² – 3x²) dæ = 0

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Q: x6(xy)² xy-1 If Find: a = b= is equal to xayb

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Q: 7x d.x 2)3 (1 – x²)³

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Q: d) 2х3у + e2y — 4х + 5x2. e) y = (2x* + 4)*x %3D

A: We have to find the derivative

Q: (3-5x) 2. (3- 1y(r – 1) d (3х - 1) (х —1)2

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Q: (x² + 6n") da - 4 xydy こ0

A: Solution is  2y2= x2logx+2x2

Q: Help solve all 3

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Q: x3+6x-2 6) S- x++6x2

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Q: III Find y" if y=2x- 4x-x²+7 120x -24 A O B O x² - 4 120x+24 D. x²+4

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Q: 1. P(3)= x³ - 3x² – x+ 2 %3D 2. P(-1)= 2x³ + 2x? - 4x + 1 ||

A: Given the polynomials, we have to find p(x) for each given function using Synthetic Substitution.

Q: x(n) = 3 [2n + 4″]

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Q: 4. r(x) = 7 + (2x + 1)³ find r(x) %3D

A: Given that r(x)=7+2x+13         ...(1)

Q: 3. y² = -x, x² + 3y + 4x+6=0

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Q: " g(x) = V3x2 + 4x + 1 %3D

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Q: 2x e y = 2x y = (3x² – x).(*2) 5x+2 y =

A: Here we have to find the derivative of the given two functions.  In first function we use chain rule…

Q: 16(x* yz)ª (2x")

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Q: x* +2y* %3D 3

A: Given differential equation is homogeneous do put y =  vx

Q: (e) y"+4y' = -4y %3D

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Q: 3x g(x) : %3D (х — 5)(х + 4)

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Q: x² + 1 If y then y' will be = 2x – 3ex'

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Q: z) if - 11z - 75 | and g(x) %3D T2 + 10x + 2 separate your answers.

A: We have to find the value of x according to the given information

Q: аx2а (х2а+1)* dх ax²a

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Q: = x²e2= 2x- %3D nd

A: Partial differential eq: w=x2e2x+3yWe need to find ∂w∂x|(1,0)

Q: 8. . x² = 4y and y %3D x2+4

A: As per the guidelines I can solve only first question

Q: 3X (02-60,9)y=e" (x+2) %3D

A: Given differential equation is  (D^2 - 6D + 9)y = e^3x(x+2)

Q: Find the consumer's and producer's surplus if for a product D(x) = 16 – 0.006x² and S(æ) = 0.003x² .…

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Q: -4x 2.) y = required:a) find the value of y if x = 1

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Q: (b) f(x) = 2xvx +1 %3D

A: To find the local extreme values we will use 2nd derivative test.

Q: 3. g(x) = x³ + 9x² + 25x + 17 %3D

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Q: 6. y = V2x – 3x . Find y'" -

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Q: 2 p4 p2 0 -1 (8x-2y+z)dxdydz

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Q: 2x + 2z = 12 x-z =4 provide a graphical solution.

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Q: Find the complementary solution: (D^3+D)y=x

A: QUESTION- Find the complementary solution:   (D^3+D)y=x

Q: 9. P(x) = x* – 2x² + 3, d(x) = x + 2 %3D - %3D

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Q: 1. (t. xp- 2x 1 а. 3 /x. + C b. (1+x)³ + C 3 X + C с. 2x(1+x) d. None of the above

A: Given integral is, ∫1+x2xdx.   It is integrated as follows:   ∫1+x2xdx=∫1x+2+xdx

Q: y = In(x² + 4)

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Q: c. y = x° - 4x 3 %3D

A: Given: y=x3−4x

Q: 12) m22 = 6x – 4 and m/HFG = 10x + 6. Find x. %3D %3D | H. F

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Q: x² +3x -4 g(x) = %3D x+1

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Q: (x³ – 9x2 + 16x – 144)y?dy (2x2 - 1)e4dx %3D

A: We will find out the required solution.

Q: (4x-2)2n+1 a) E (-4)" (x-2)". V2n n! b)

A: Given: ∑n=0∞4x-22n+1n! ∑n=1∞-4n2nx-2n

Q: 8x + 1 r(x) %3D 4x2 + 1

A: Given: rx=8x+14x2+1

Q: (4) y" – 3y +2y = 1+e² %3D

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Q: y" - 3y' +2y = e4x + 6x3 – 2+ 3sin(4x)

A: We have to find CF and PI

Q: 3. y'-5y=x²e* – xe*

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Q: 2. y" – 2y' - 3y = e2x + 3x² + 4x – 5 + 5cos(2x) %3D

A: We have to find the general solution of differential equation

Q: e*+3x-4 mx→0 3x+1

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Q: f(x) = 5.2x + 2.3 %3D

A: To differentiate: f(x)=5.2x+2.3 Solution: