5-8 Find the derivative and state a corresponding integration со formula. 5. dx [Vx +51 6. dx x2 +3 d 7. [sin(2V] 8. -[sin x-x cos x] dx dx

Q: Sa 2x²+2+x³+x² =dx = [Aƒ (x) — B ln(g(x)] + D fb dx, and if A = ,B<0, then f(x) dx x+2 x² 2x + + 5…

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Q: 5. 6. Solve fo e-t sint dt. dt. t Solve fe-t. -t sint t

A: Disclaimer:  Since you have asked multiple question, we will solve the first question for you. If…

Q: 12 Solve the equation. d²x dx + 4 + 3x = e-3t dt2 dt dx given that att= 0; x =} and = -2. dt

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Q: Solve for the derivative of the Hyperbolic Differentiation. 1. y = ex cos h 2x 2. y = ln sin h x…

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Q: dx 4. -' (x- 3)*

A: Solution is given below

Q: 3x – Vx + xp+x- а. 2 34 -3 In x+ C 3 3 O b. 2 2 -3 In x+ C 3. c. + 3 In x + C 3 d. x'+x* +3In x+C +3…

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Q: *+1 dx = 0 3- xex dy +- y

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Q: f(x) = cos(x) + 2 sin(x) + x² Use the Newton's method of finding roots of equations to find the…

A: Given: fx= cos x + 2 sin x + x2 Initial Guess x0=-1 and x0=1 Error as 3% To find: The roots of the…

Q: 2х + 3, х oʻ Evaluate ,f(x)dx. . Given that f (x)

A: First break the interval of integration. Then open the mode. And integrate it..

Q: dy Solve x - 4y = x°e*. dx

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Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: :) 3 1 19. + dx x3 3x 20. | (2.x2 + x – 1)dx 2y4 + 1 / 2y4 Зуз 21. ip- 1 1 22. / (VE+1- + sin x – e"…

A: 19.  Let the given be I  I = ∫3x3 - 2x3 + 13xdx Now integrating given integral , we get  ⇒I = ∫3x-13…

Q: dv = dx = v=x V = 1-a'x 1-a'x

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Q: Find the derivative of the function. 3 y sec² x 5 a. y' sec? x tan x b. y' = sec? x tan² x sec" x 5…

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Q: Mu=Φ x 0.85 x fc' x a x b x (d - a/2) 266000000 = 0.9 x 0.85 x 21 x a x 366 x (486 - a/2) a= uknown…

A: As per the question we are given the following equation :266000000 = 0.9 × 0.85 × 21 × a × 366 ×…