y ≥ 4/3x − 4

Q: |3 Sm2万x d x'ln tz de

A:

Q: y' + 2y = e*,

A: Note: Since you asked multiple questions, I solved first one if you want answer of other questions…

Q: 13 [* Vx2 +y dydx 00

A:

Q: Differentiate. h(x) = In(xe-2*)

A: First simplify the given function using properties of lograthim than simply take the derivative.

Q: xsin-1x > [4) S*s dx [4] S Y1-x2

A: Here is the solution

Q: Simplify

A: Given: To simplify the expression       (2x2 y-5) (6x-3 y)…

Q: 6 iven differentinl ....(1x) dx = 2x+y with (2*)

A:

Q: S(x - 2x –1)dx – 2x-

A: In integrate by using formula for general case.

Q: Calculate y*)(0) for 0 < k < 5, where y = x* + ax³ + bx² + cx +d (with a, b, c, d the constants).

A:

Q: of Chal) D x24 6x -2:0 ent

A: Solve x2+5x-2=0

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

Q: S 2dx x(3(Inx)"+1지lnz-15)호 2 +13/nx-15)

A:

Q: Find ax dy x-2–1 given y = 2x3

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Q: 13. S: 5x dx x5-3

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Q: 11-x 1 S S S dydzdx 00 x+Z 2.

A:

Q: 2. x y-3xy = 4x + y+1 at (0, - 1)

A:

Q: dzy dy +4 +4Y = X•ē=X Xp dx2

A:

Q: 2dx x (3(ln x)2 + 12 In r – 15)

A: Indefinite Integration

Q: 7). Sx² sech x³ dx 3

A:

Q: Differentiate. y = In [(x + 4)(3x- 2)(5 – x)] d In (x+ 4)(3x – 2)(5- x))] = || dx

A: We have, It is known that the derivative of ln(ax) is, and derivative of the function of u.v form…

Q: 2 + 3x + x) dx . 3x² + x) t 3

A:

Q: 2. (a) Evaluate [ x* V1+4x² dx. (b) Evaluate 8x° +13x dx. (x² +2)²

A: (a) We have to evaluate the following integral: ∫01x21+4x2dx Then we get,…

Q: 2 d'y If y = 3x 4 4x + 18x find 2 dx

A:

Q: #1) Find for 7x³y5 = -8 dx

A: Let's find.

Q: 3r² + 10x + 7) In (z²+3) dz

A: I am attaching image so that you understand each and every step.

Q: (x4 - 4x²y²-y4) dx + 4x³ydy = 0; when x = 1, y = 2

A:

Q: 1. x = y =. M 31 L5y9

A: Triangle properties

Q: if fcx) : gex) = X 11 X+ 1 find DE n Dg 2.

A:

Q: 7. Solve: dy x + 3y dr 3x + y

A:

Q: Q2: Find for y= (4x² +12)²(3x-20)² dx

A:

Q: (iv) S: (1-x²)z dx x8

A: Given:

Q: dy 4x2 + x dx y + 4

A: Given : dydx = 4x2+xy+4

Q: -.f x³ ex² dx 3

A:

Q: x y3 (2ydx + xdy) -(s ydx +7X dy)=o

A:

Q: S (2 + x)dx √4-2x-x²

A: We can solve the integration as below.

Q: II. Solve xdy + (3x – 2y)dx = 0 in two ways

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Q: 4x3+x dy x 1+2x²410

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Q: y, = x2 + 2x + 2 Y2 = 2x + 18 dx 25- 20 15 y 10- 5- 6.

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Q: 4. y = vx + 2 x,for-

A:

Q: (2) S 1 x= V1-x²

A: Solution

Q: Find d^2y/dx^2 for y=2x^3-5/x^2

A:

Q: 7. Solve: ydx = 2(x + y)dy

A: Answer

Q: x2+5x+4 If y(x) = In find y' (x).

A:

Q: II. Solve xdy+ (3x – 2y)dx = 0 in two ways.

A: We have given differential equation,  We have to solve it using 2 ways,  1st Method: It is of the…

Q: 11. Find y'if y = 2x + Vx* – 9x+3

A:

Q: Find y' given y = (x³ – x² + 3x + 10)S

A: