15. For y=2x-x², x = 2 and Ax= -0.4. The value of dy + Ay is equal to (b) (c) (d) (e) 1.44 0.16 -0.16 -0.44 -1.44 X = 2 X+ DX = 1₁6 (correct)

Q: (c) J xe0.4x (0.4x + 1)2 d dx

A:

Q: 4. If f(x) = 23x1, what is f(-1)? а. 16 b. 1/16 с. 8 d. 1/8

A:

Q: 7. Find d²y dx² from y = √√x- =√x-²/2

A:

Q: 2 3 Find 3/7 ) da 6x2 | _ -

A: We need to evaluate the following integral ∫6x2-2x+3x5-3xdx

Q: 7. Use substitution to evaluate ſ 2x(4 – x²) dx.

A:

Q: (x-2)² + (y+1)² =16, find- A. 16 (y+1)³ d²y dx² B. 16 (y +1)³ C. 16 y³ D. 16(x-2)² (y+1)³

A:

Q: dy 5. x- 3y = x². dx

A: (5)We need to find the solution of given differential equations

Q: 6. Find y = f(x) given d²y = 5x? + 2 dx2 %3D

A:

Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: 3. 1 x2+12x-5 (x+1)(x-7) dx

A: We need to solve the following integral I = ∫x2+12x-5x+12x-7dx…

Q: 5. Solve for x² − x+6 x³ + 3x 1³ dx.

A:

Q: S(x+ )´ dx 2 1 X X.

A:

Q: 10. (D² – 3D) y= 9x² = 9x2

A: 10) Given Information: Given differential equation is D2-3Dy = 9x2

Q: 4. dx √-x² + 6x

A: 4.We need to evaluate the following integral,⇒I=∫dx−x2+6x ;

Q: √ 1 x²√2x-x² dx = x+¹√ √√2x-x² + c 3x²

A:

Q: 10. ff(e²x + x²)dx

A:

Q: 3. (0.002x4 -0.3x² + 4x - 7) dx

A: The given integral is    ∫-1010(0.002x4-0.3x2+4x-7)dx

Q: 2f(x)dx = - 4 and | (F(x) + 1)dx =7. Then | (3f(x) – 2x)dx = Select one: а. -2 b. 19 С. 10 d. 13

A: ∫-122f(x)dx=-4 and ∫-13(f(x)+1)dx=7. find ∫23(3f(x)-2x)dx

Q: 4. x(x² – 1)² dx

A: Solution:

Q: Sx V(x² – 5) dx 3 2

A: We have to solve the given indefinite integral: ∫x x2-53 dx Solving the integral by using…

Q: Y = -2X, then p(X, Y) = 1?

A: Solution

Q: 3 4. S (x+3) z²+1 5 dx dar.

A: As per bartleby guidelines we only give first question answers. Please repost for other parts.

Q: 3. fz √z dz 4. (2x² 3x + 5) dx -

A: 3. ∫zzdz4. ∫2x2-3x+5dx

Q: 1 14) Find xe™³x² dx . | 0

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Q: 3.ƒ _(x−1)² dx √x

A:

Q: 11. For y = X 2+x², determine d²y dx² when x = 1.

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Q: x2 (C) S²_₁₁√x+2 -1 dx

A: To find ∫-17x2x+2dx

Q: Differentiate y = [e2x + (x + 1n x)3]4.

A: Given function is y=e2x+x+lnx34. Power rule of differentiation states that: ddxxn=nxn-1 Chain rule…

Q: 1. Solve. X x²-5 +5r+0 - dx

A:

Q: 12. (x' + 5x + 4)dx n= 6 0.

A: We have to find the given definite integral.

Q: 353. y = x-1/2 (x² + 3)2 (3x – 4)ª

A: First, we expand the given expression using properties of logarithm

Q: dx 1. (x-3)(x-2)

A: Given I=∫1x-3x-2dx To evaluate the integral I: