Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: (c(2z+y), %3D ue of c in the joi F of W.

A:

Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

A:

Q: The linear approximation at z = 0 to sin(8x) is A + Bx where A is: %3D and where Bis:

A: Given : The linear approximation at x=0 to sin(8x) is Ax + B   To Find : Value of A and B

Q: The integration of ſ, Vx tan-'Vx dx is

A: Given that  The integral is

Q: Integrate by Substitution. 1. dx where u = Vx+2 2Vx+2

A: By using substitution method, we calculate the given integral.

Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: sin(2t)dt 0,

A:

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

Q: The integrating factor of the LDE y'=x-2ycotx is A B с D sin²x sec²x csc²x cos²x

A:

Q: Reverse order, then integrate SaE ) dydx. Vx \1+

A:

Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

A:

Q: Find the orthogonal trajectories of r= a sin? 0 where a be the arbitrary constant.

A: We have, r=a sin2θ .....................................................(1) Differentiating w.r.t.…

Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: Find ds/dt when u = 3pai/2 if s = cos u and du/dt = 5.

A: Given,

Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

A:

Q: |dx + N(x,y)dy = 0 x² + y,

A:

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

A:

Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

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

A:

Q: TIJY sin /x dx dy by using the transformation u= Vy. v= Vx ? 0 0

A:

Q: I = f, (sinhz + 1)dz. %3D

A:

Q: Use the Chain Rule to find az/ðs and ôz/dt. z = arcsin(x – y), x = s² + t?, y = 2 - 2st as az at II

A:

Q: Find the Second appoximation for the System. X Sin y at (xo,,)= (1, 1). y=Cosx

A:

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 ), x = 4 sin(t), y = 6 cos(t), z = 5 tan(t)…

A:

Q: Use the Chain Rule to find dw/dt. w = In Vx2 + y2 + z2 x = 2 sin(t), y = 5 cos(t), z = 4 tan(t) dw…

A:

Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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

Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

A:

Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: Find the Saution of the equation using Inver's operator method y + 3y + 2Y = 4 cos(x)

A:

Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

A:

Q: X Cos 9TTX² dx 2. 2. V= dTx²

A:

Q: integrate t dt/(1-ct) where c = const.

A: Solved below

Q: Calculate the Cauchy principal value. 8 COS X V.P. Leta -dx, (a > 0). (a²-x²)

A: We solve by using residues.

Q: Verify the linear approximation at ( 0, 0) for e^x cos(xy)

A:

Q: Find dy/dt. show all work y=cos(square root of 8t+12)

A:

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

A:

Q: Use the Chain Rule to find dw where w = sin 8x cos 2y, x = , and y = t°. dt 2 dw dt (Type an…

A:

Q: Find dy/dx in terms of x and y if cos² (4y) + sin“(4y) = y + 8. %3D

A:

Q: ds Find where Vt +s = 2s . %3D dt

A:

Q: Find the intergral of  (t^2 sin(t)cos(t) +t sin^2 (t) )dt

A:

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

A:

Q: Find LT for f(t) = sin²(wt), f(t) = cos²(wt) %3D %3D

A: We need to find the Laplace transform of ft=sin2wt and ft=cos2wt Now, before finding the Laplace…