D={(x,y):4 < x² +y² < 81,< x <-V3y}, V3 Find [S, dA JJp y2

Q: zy dy de t 5/2/2/0

A: To evaluate : ∫032/2∫0xxy dy dx+∫32/23∫09-x2xy dy dx The general formula of integration is…

Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: t2 + 4t + 10 -dt t3 + 2t² + 5t dy J 3 + 5cosy

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Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

Q: Q) Find y" + 3y 5y at x-5 where y = xsin(1/cscx))

A: NOTE- AS THE SECOND QUESTION PICTURE IS NOT CLEAR SO I AHVE DONE ONLY FIRST QUESTION. IF YOU WANT…

Q: IND THE ORTHOGONAL TRAJECTORIES OF THECURVES Y =Cx²,WHERE CIS AN ARBITRARY CONSTANT.

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Q: Find the length of the curve y = Vcos 2t dt from x = 0 to x = T/4.

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Q: 0. dy for y = 4t dt. 4t +1 3x3 Use Leibniz's rule to find хр

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Q: (b) Integrate f(x, y) = 4e0.8x - 0.5y using h = 0.5 with y(0) 2 from x = 0 to 0.5.

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Q: Find dt y = 6t + /9+ 7-t dy dt |3|

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Q: Find the total differential. w = (3x + 4y)/(y + 3z)

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Q: Q4) Find y" + 3y' 5y at x=5 where y = xsin(1/cscx))

A: Solution:-

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/escx))

A: To find the y"+3y'×5y at x=5  Given y=xsin(1/cscx)

Q: xy ,show that: x- y If z = = 0

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Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: dy dt 1. y=V(3t2 - 2t + 1)(t2 – 1), 12/07/2021 18: 54

A: Given that       y = √(3t2-2t+1)(t2-1)  Here we have to find dy/dt .

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

A: As you post multiple questions According to the guideline I only solve the first problem. Please…

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

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Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: d²s ds + dt 4t + 2cost where s = 0, ds/dt = 0, t= 0 dt2

A:

Q: Let y = v2x. Determine the point (x, y) that is closest to the point (5, 0). That is, deteremine the…

A: find the minimum distance from a point

Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

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Q: Find the total differential. 4x + y w = 2z - 8y |

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Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

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Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: d²y csinx Find if t Vt2 + 5 dt + sinx = y – x secx dx2

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: Q4. Find dz/dt where z = 2xy - x² y² and x = 2t, y = t²

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Q: 3e2º sec 20 dy determine de Given y = V(0-2)

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Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: At what interval is y=2x4- 4x2 concave downward? Ux> 3 3 3 3 V3 3 <x< 3 3 <x< V

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Q: Suppose that f(0) = 1, ƒ(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Q4) Find y" + 3y' 5y at x-5 where y = xsin(1/cscx))

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Q: C(x) = 1500 + 13x – 0.1x2 + 0.0005x3. - %3D Find the marginal inal cost finctien?

A: Given query is to find the marginal cost function.

Q: Find f fy. - f(x.y.z) = x - Vy² + 22? + 2z² = (Type an exact answer using

A: Here we have to find fx , fy and fz  of

Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

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Q: Q9. Find y2 using Reduction of Order y" – 3.ry +4y = 0, Yı 1 = x?

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Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…