Given the implicitly defined function sin(a*y) + y = + y dy dy and find at the point (r, y) = (0, 1). %3D dr2 dr3 6.

Q: If x? + y2 = 100 and dy/dt = 9, find dx/dt when y = 8. (Enter your answers as a comma-separated…

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Q: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: 4. Evaluate: S. yx?dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t2 , (0 st< 1).

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Q: Use Runge-Kutta 2nd order to find y at x=2, given that Fill in the table below with your result?…

A: Introduction: The formula of the second-order runge-Kutta method is given by, k2=hf(x0+h,y0+k1)

Q: M(x,y) dx + (x,y) dy=0 to be exact

A: Solution :

Q: Given x = 2 In(t) and y= 4 t then find dy dx dy da?

A: Given, x = 2 ln t  &amp;   y =  4t2

Q: Use Euler's method to find the approximate value of y correct up to 4 dy =x-y² decimal places for…

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Given the equation x +2xy + y° = 8, evaluate dy Assume that the equation implicitly defines y as %D…

A: The objective is to find the derivative.

Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

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Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: Given Volume of cone isV=13πr2hwhere r is radius and h is height and h is constant .

Q: Given I 2 cost +35 and y = 6 sin' t dx %3D dt dy dt dy dx ||

A: Given: x=2cos t+35y=6sin2t Therefore, dxdt=ddt2cos t+35       =-2sin  tdydt=ddt6sin2t       =6(2sin…

Q: a) Solve etan y dx + (1+ e*) sec'y dy = 0. sin(3z + z?) b) Find y for y = (6 – z*)3

A: The given differential equations is  and the other equation is y=sin(3z+z2)6-z43 The differential…

Q: ²+ re" = 2y + e² %3D

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Q: Given x 13t - 12 and y = 169 sin t %3D %3D dy %3D dx dy dæ?

A: Given that       x = 13t - 12   and   y = 169 sin t Here we have to calculate     dy/dx         and…

Q: ;(y+ 1) e*dx = (e* + 1)y dy, what is F = 1.F. J (-e*y - y)dy? %3D

A: Given: y+1exdx=ex+1ydy

Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: Given the equation dy = 3x2 +1 with y (1) = 2 %3D dx Estimate y(2) by Euler's Method using h = 0.5…

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Q: W3:- Estimate y(0.2),using Euler methe ere y': = -y?cosx „y(0)=1

A: Here we have to estimate y(0.2), using the Euler method with step size h=0.1 where,

Q: If the D. E. + M(x, y))dx + sin(xy)dy = 0 is exact then the function М(х, у)

A: If the Differential Equation 1y+M(x,y)dx+sin(xy)dy=0 is exact then the function M(x,y)

Q: Find  dy dx at the value of the parameter. x =    t,  y = 2t + 8,  t = 16

A: See attached file for a step by step explanation.

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

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Q: Given z= 2 cost+6 and y= 5 sin t dz (i) dt dy (ii) dt dy (iii) da

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Q: For the curve y = f(x) = x², 0 ≤ x ≤ 2, its length is 2 L = 1+ dy dx dx =

A: Given curve y=f(x)=x2,0≤x≤2 The objective is to find the length of the curve.

Q: Find dy/dx implicitly and find the largest interval of the form -a <y <a or 0 < y <a such that y is…

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Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s…

Q: b) Find fo dy for y = Vt-1 t = sec?x sint

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Q: Given that x cos y + y cos x = 1, find dy/dx.

A: Given that, xcosy+ycosx=1. The objective is to find the implicit differentiation of xcosy+ycosx=1…

Q: 3. Given a function z = x2 + xy°, and x = cost, y = sin t, evaluate when t = T. dt

A: Given,            A function z=x2+xy3 , and x=cost , y=sint

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: Given equation, V=13πr2h                          ...(1)

Q: Assume that y= sin dy 'x is a differentiable function of x. By differentiating the equation x= sin y…

A: Given,           Assume that y=sin-1x is a differentiable function of x. By differemtiating…

Q: Find the area between the two curves.

A: The area between the curves y=sec2x and y=sin2x on interval 0, π4:The area between curves is the…

Q: Given z = 2 cost +3 and y = 3 sin?t da dt dy dt dy da

A: Explanation and solutions is given below....

Q: Given f(x, y, z) = xe"y + sin(xyz), find fyzz

A: Derivatives of: Sin x is Cos x Cos x is -Sin x u

Q: Find the value(s) of dy at y=1 given that x²y+y² =5. dx only only D

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Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: Given z = 2 cost +35 and y= 9 sin t da dt dy dt dy dx %3D %3D %3D

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Q: · Use Euler's Method to solve the following problem over the interval from x = 0 to 1.0 using a step…

A: Given, f'x,y=dydx=2+3xyy0=1 Euler's method is given by, yn=yn-1+hfxn-1,yn-1

Q: Find the value(s) of dx at y= 1 given that x²y+y² = 5. only В only 2

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Q: Given x = 2 cost +33 and y=8 sin t |3D da dt dy dt dy dx

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Q: d?y by implicit differentiation, given x³ + y³ = = 8. Find dx d?y dx2 dy 8,

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Q: y sin x – xy = C

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Q: Given the eguation y In (x +y + 1) = 8, evaluate dy Assume that the equation implicitly defines y as…

A: Differentiate with respect to x

Q: Given the equation y In (x+y" +9) = 5, evaluate dy Assume that the equation implicitly defines y as…

A: The given equation is  y.ln(x3 + y4 +9) = 5 To find dy/dx

Q: dw b) If w = (x + tanx). (Vx – 1), and x = tan (cost) find dt

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Q: Assuming y is a function of x, find dy/dx for 5x sec(y) – 3y sin(xy) =e^(5xy)

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