dx = 6, find dt dy Ify = 2x3 + 6x and whenx = 4. dt wwww A 582 782 None of these D 822 E 732

Q: dN F(V)dV = = 4x(- N -3²v² exp(= `2 TRT ` 2RT AP(- where dN, the number of particles having a…

A: Given: F(V)dV=dNN=4πM2πRT32V2expMV22RTdV Now, V2=∫0∞V2f(V)dV         =∫0∞V2 4πM2πRT32V2expMV22RTdV…

Q: d'x dx Solve the equation + 2x = e given that x (0) = 0, x' (0) =1. +3 dr dt %3D

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Q: 10. Evaluate: +4x dx (a) (b) (x2 -2x 4) dx (c) (t2-t) dt (et cos t) dt (d) dx

A: Here, we use the formula that integration of x^n is x^(n+1)/(n+1) as shown on board.

Q: dy dx -3х а) +3y= 2xe3* b) t- +3x = 2t°, x(2) =1 dx dt

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Q: 5. (x* +a')dy= 2x| (x² +a²) +3y dx, where a is constant.

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Q: 3. If 2 = x² – x* + 6x – 5, then dty evaluated at x = 1 is dx4 dx (А) 8 (B) 36 (C) 96 (D) 120

A: To calculate the nth derivative of function y, differentiate y four times with respect to…

Q: dx 15 √(x+2)(x-1)²² -S[ +42 + (A) 93 B (C) (D) 12 93 —— . 2 3 2 3 B x-1 + (x −1)² ]dts dx, the…

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Q: dx dy =1.95. dt Given y = x. Find when y= 3 and %3D - - dt (Simplify your answer.) dt

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Q: dx Given dt 1 and y = 6. Find for x2 + y² = 100 dt O A. 3 4 O B. 3 4 3

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Q: dx -0.16x + 0.08xy dt dy 4.5y – 0.9xy - dt

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Q: dx 1.5- 2x-x e if y = r(In x)² . . fr'e* dx. 2 if y = csch-1 20. de 2x+2 dx. -2x+1

A: since you have posted question with multiple subpart s, As per our guideline we supposed to answer…

Q: e2x -dx =D 1+ex (A e2x + In(1+ e*) + c B 2e2x – In(1+ e*) + C © e2x – In(1 + e*) + C D ex- In(1+ e*)…

A: Integration

Q: dx 2*+1-5x+1 (a) (b) [ cosh*x dx, (©) Jarcsin x)²1-x² dx, (c) 10* [In(v + 1)]² v +1 (e) T20 -02 (d)

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Q: d²y Find particular solution for + 4 + 4y = 3xe dx dx

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Q: dy Find dx 4t t dt + 2 y = dt - t° + 2 - 3 6. dy dx (Simplify your answer.)

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Q: dy = 4, find dt dx dL If L=Vx2 +y dt when x = 9 and y 12. 5, dt dL (Simplify your answer.) dt

A: our objective is to find the derivative

Q: oð 7 T R S4 # 3 Let y = 3x?. Find the change in y, Ay when x = 3 and Aæ = 0.2 Find the differential…

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Q: choose the correct answer If y = t^2/(t^2+1) and t= √(2x+1) the dy/dx =

A: Given, y = t2t2+1   and  t = 2x+1 We have to find dydx.

Q: 3. fy dy + 10g = e + dt +7 -2t

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Q: x^2+3y^2+4y=19; dx/dt=7 when x=2 and y=-3; find dy/dt dy/dt= simplify the answer…

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Q: dy 9. = 2+ e dt

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Q: dy 5. dt = e&-t)secy(1+ t²). %3D

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Q: Calculate  dy dx.  You need not expand your answer. y =    x2.3 5 +  4 x2.3  (5x − 1)

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Q: dx %-D5 when x= 4. dt ,3 Assume that x x(t) and y y(t). Let y=x +2 and dy when x= 4. Find dt dy…

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Q: 1² + 3x + 4 If t = (r² – 1) what is dt/dx?

A: We have to find derivative

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 9x2 − 3   dy=?

A: The given expression y=9x2-3 Differentiate both sides with respect to x dydx=d9x2-3dx     =9dx2dx-0…

Q: dx 1. dt 2х + 3у — 7 dy —х — 2у + 5 dt

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Q: dy 1 andy 3x? + 1 if- dx Find- atx = -1. dt dt 1 6 -6 ||

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Q: d²y d²x 9. х y = C1• %D dt2 dt? di 10. L-+ Ri = E. dt 11. (x + y)dx + (3x² – 1)dy = 0.

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Q: dy Solve the ODE: dx 1+ y? Solve the IVP: ty' + (t+ 1)y = t, y(ln 2) = 1, t >0 0

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Q: d²y 34y +2y=e" – 3 . dx dx Find the general solution for

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Q: ed²y "-xy+e*(1+ 2x) = 0. dx? dy 6. (a) If y = e¯* In x , find Then show that x dx

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Q: Solve for dy/dx if x = 2 + t and y = 1 + t2   a. 2t b. 2 c. 4t d. 2-t

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Q: d Q. a Vi In(t)dt equals dx a.36a6 (In x) – V2 In(2) b. Væ6 In(x°) – V36 In(3®) c. 6x² (ln x) d.36x7…

A: Using the chain rule and the fundamental theorem of calculus here.

Q: d Q. A Vē In(t)dt equals dx a.36x6 (In x) – /2 1n(2) b. V#6 In(x®) – V36 In(3®) с. 6х? (In a) d.36x"…

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Q: e2x -1 If y = In find dx dy e2x +1 ' Select the correct response: 2e2x e4x+1 e2x e 4x+1

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Q: d²3 Find the particular solution of +16y=0 if given y(0) =1 and y'(0) = 0. +8 dx dx

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Q: (e) S -dx, x = 3 sec t Ans. C + Vx² – 9 – 3 sec¬1 () (f) x² + 4x – 5 -dx

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Q: dx + 3t?x = x?t et3 solve by Bernoulli's dt Equation

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Q: dy for e dx (*² +1), 6. Determine ln( 19) + x² – xy =

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Q: dv 9. S- V3v-2a 10. S(5 – 3y)*dy

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Q: 4e4sin6x dx secбx Evaluate A) -In|sec6x| + C B 4sin6x + C 1 e4sin6x+ D 4In|sec6x| + C

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Q: dN = 47(- N MV² -)dv 2RT M -)3/2v² exp(- 2 TRT F(V)dV : where dN, the number of particles having a…

A: Given: FVdV=4πM2πRT32V2e(MV22RT)dV Obtain: <V2>=∫0∞V2fVdV Compute the integral with…

Q: If y = In dy then dx 10 10 20 et - E) eT – 10 A) x – B) eT D) 0 eT – 10 10 — еT Of –

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Q: dy/dx=(x-7)e^(-2y) satisfy the initial condition y(7)=ln(7)

A: Use separation of variables to integrate.Given:

Q: dx (b) (t– 2) – x = (t – 2)' , x(4)=10 dt dx (c) +5x -t = e" , x(0)= dt

A: Here we have to solve given initial value problem b and c.

Q: xy = 2 (a) Find dy/dt, when x = 8, given that dx/dt = 14. (b) Find dx/dt, when x = 1, given that…

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Q: dy dx Suppose x and y are functions of a third variable t. If 2sin(x) + 4cos(y) =3 and dt -3, what…

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Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

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Q: Solve dx/dt+3x=e^-2t given that x=4 when t=0

A: dxdt+3x=e-2t Comparing with dxdt+Px=Q, we get P=3  &  Q=e-2t Now integrating factor is, I.F=e∫P…