2. (1 point) If § f(x)dx = 12 and f(x)dx = 4 then which of the following statements is FALSE? (A) f(x)dx = 16 (B) S f(x)dx – 3f (x)dx = 0 (C) f(x)dx = -12 (D) L f(x)dx = –4 (E) f f(x)dx + f° 3f (x)dx = 16 %3D

Q: f(x) dx = -4, f(x) dx = 6, g(x) dx = 8 - If g(x) dx b. c. 3f(x) dx d. dx x) - g(x)] dx g(x)] dx e.…

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Q: 3. YA x=y² – 2 ソ=1 x= e' y=-1

A: Solution Question 3  Given,  The curves  x = y2 -2    and   x = ey We have to find the area of…

Q: dy If 3x -1 and if y= - 1 when X=1, then y= dx A x³ - x-1 x³ +1 © x³ - x+1 D -x3 + x-1

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Q: Example 2: Solve (y + x)dy + (x – y)dx = 0 .

A: The given differential equation is y+dy+x-ydx=0. Simplify as follows.…

Q: If If y + x³y3 =y e\ + 1, y is function of x, then dx 3 x²y³ - y e* 5y* – 3 x³y? – e* 3,2 O 3 x²y³ –…

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Q: 3. (10 – 6y +e 3) dx -3x 2dy = 0 -

A: According to our guideline, we can solve only first question of multiple question. If you want…

Q: B) dy = 8xex2. 9) y = e4x² + x A) dy = 8xe2x + 1 dx B) dy = 8xex2 + 1 %3| C) dy = 8xe + 1 D) dy -…

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Q: 4 (iv) F(s) = s2 +9 2s + 16 (v) F(s) : s2 + 4s + 20 3s – 15 (vi) F(s) %3D 2s2 – 4s + 10

A: The Laplace transform of a function is an integral that converts the real variable into complex…

Q: dy -is If y = In(x-5), then dx 4x x-5 4. 3x 4 x-5 4x 3. 4x +5

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Q: 2 The derivative of y = 3x? 3 + 3x is 2x 3 A. y =** 2 2 3 x° + x´ +3 3 4 4 В. у B. y' = +3 2x2 + 3x…

A: Derivative.

Q: '2 (c) f(x) dx -2+ 2n (d) f(x) dx -4 2(1–n) (e) |F(x)[ dx 2 (π-1)

A: Since you have asked multiple question, we will solve  first 3 subparts of the question for you as…

Q: ことる ーx (x+2)(X-2) -6x (x -ax+4) y" CX+2) (x-1)3 need first derivative Eanalysis %3D (x-2)3 (x+2)°

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Q: d²y dx² 2 (2x-3)² Find y = O O d²y dx² d²y dx² d²y dx² O d'y dx² = = = = 12 (2x-3)¹ -12 (2x-3)4 48…

A: Given equation is y=22x-32. Find the value of d2ydx2. Here we use the differential formulae:…

Q: [g(x )cx = 2 If then g(x )dx equals

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Q: 4- Determine an expression for dy/dx. 3(y-2)3– x= 4x - 6.

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Q: d. yı = X1 X3 X1 + X2 Ya = - X1 – 3x2 – 2x3 e. yı = x1 + 2x2 + X3 Y2 = Y2 = x1 + x2 Ya = X2 + X3.

A: d)  The map from R3 to R2 is onto.  e)   The map from R3 to R3 is not onto.

Q: A) xy' 2y + x'e*

A: These are all unrelated & lengthy problems. By Bartleby policy I have to solve only first one.

Q: If f, g L₂ then [S* S(x)g (x) dx ] * ≤ [f*° ƒ^²(x)dx ] [1° g² (x) dx]

A: This is the famous Cauchy Schwarz inequality for integrals. It follows by working with quadratic…

Q: 1. f'(x)dx if f(2) = 1 2. f(x) = S(x² + x – 3)dx if f (2) = 3 3. f(x) = S xe*dx if f(2) = 3 4. f(x)…

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Q: 10 10 10 [3f(x) + 4g(x)] dx. Jo If f(x) dx = 33 and g(x) dx = 14, find

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Q: (1) If f(x) = { 3 x2 ; -1<x<2, then 0 ; otherwise compute [ xf (x) ]dx and [x²f(x)]dx

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Q: 4. If Kx)dx = k, ] fx)dx = (x-f(x) )dx what is the value of Ax)dx? Use: [Ax) - g(x) ]dx =[ fx)dx-J…

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Q: Evaluate (D^2 - 3D + 2)y = (1 + e^-x)^-1.

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Q: -1.5 -4.5 -1.5 Let [ f(x)dx = 5, |_^*^* f(x)dx = 6, [*¹*³ f(x)dx = 5. -6 -6 Find and -3 [²₁ f(x) dx…

A: This question is related to definite integration, we will solve it using given information.

Q: Find the function y(x) satisfying -8/9 = 6x dx and y(-1) = - 4. dy :-8/9 The function y(x)…

A: Integrate the equation dydx=6x-8/9 with respect to x.…

Q: 21 dy d²x = 2(3+x² 2 dy xy)/x³

A: See the attachment

Q: -2 27. The first derivative of y = is (4x+1)3 а. -24 b. 24 C. -6 d. (4x + 1)* (4x + 1)* (4x + 1)*…

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Q: x2 + 2x + 4 dx 3-Jx– 1)(x² + 2x + 1)

A: Convert rational function into partial fraction. And than integrate function.

Q: Assume that a factory can produce a quantity 2x3 + x°y + y4 of goods, when x is skilled workers, and…

A: Here we use the concept of implicit differentiation.

Q: 6. 6. If f(x) dx f(x) dx = 3.8, find 5 f(x) dx. = 12 and %3D Answer:

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Q: 2y''' - 3y'' - 3y' +2y =(e^x + e^-x)^2

A: We have to solve the differential equation  For which we first solve the homogeneous equation and…

Q: 8) y = (x² + 3)ln 4x5 dy (x² + 3) · dx 2x² In 4x° + 5x² + 15 1 - 20x + In 4x³ · 2x 4x A) dy 2х + 1…

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Q: -5 f(x) dx = 6, | f(x) dæ = 6, f(x) dx Let = 2. -2 /" f(2) dz = Then -5 (6f(x) – 6) dæ = and - -2

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Q: 6. 9. If f(x) dx = 37 and g(x) dx = 18, find [2f(x) + 3g(x)] dx.

A: Answer

Q: 3 5. [20 points] Solve (x + y)dx+ dy=0 +x-

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Q: 5 5 4 f(x) dx %3D 8 аnd 1 If f(x) dx = 3.2, find f(x) dx.

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Q: 14 (3 3 1f y=/xL5x²–36 x15x²-36 X23x²+¥x-12 show that dy dx4 24

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Q: 1) f(x,y)= 2x² – 3y – 4 2) f(x, y) = (x² – 1)Xy + 2)

A: Solution :-

Q: ,1 .-2x +5 Evaluate | 3x 10-4x - 2y dy dx 25 3 25 26 7 27 5 28 3

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Q: 15. If y3 – xy = 5 ,1 d²y then dx2

A: y3-xy=5

Q: a) | f(x)dx = -10 %3D 4 b) f(x) dx = -10.5 4 c) f(x) dx = -17.5 10 d) / f(x) dx = 9 %3D 10 e) -5…

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Q: •7 49–x² r83–x²-y² x dz dy dx %D 0, -15+x²+y²

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

Q: 18. If x-xy+y? =3 find y" (second derivative) %3D 18 12 В. (x-2y) A. C. 12 (x-2y) (x-2y) 18 D.…

A: "Since you have posted multiple questions we will solve the first question for you. If you want any…

Q: 5 10-2z 12y – 8x dy dæ dz

A: To solve the triple integral

Q: dy If ay = -x+4x -3 and y= 2 when x = 0 then y is equal to dx A y =-1+8x y=--2 B ²+2x- 3x +2 4 y =…

A: Solve the above questions.

Q: -2x X-e -2x x+e * 2(x-e-2*) A -2x xp- x²+e¯ -2(x-e-2*) B x²+e =² -2x -2x e dx -2x x²+e-2r x²+e=2« D…

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Q: 16 15 [ f(x) dx- - ["f - [ ₁³ f(x) dx = ["f 6 f(x) dx

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Q: '5 If f(x) dx = 8 and f(x) dx = 5.3, find f(x) dx. If f(x) dx = 31 and g(x) dx = 14, find [4f(x) +…

A: 1. ∫17f(x)dx=8 and ∫57f(x)dx=5.32.∫07f(x)dx=31 and ∫07g(x)dx=14

Q: 4 1** ƒ(z)dz = 3, and [*9(2) If f(x) dx 5 g(x) dx = 3, then an [*14ƒ(z) + 6g(z)]dz ==

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