Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of path: fe %3D дд дх (12,16) – (28x³y³ dx + 35y*x*dy)

Q: 3) Graph and evaluate and evaluate 5 dx -2 7 6 و اس ام اس اب 5 4 3 2 101 -7-6-5-4-3 -2 -1 0 1 2 3 4…

A: Topic = Functions

Q: •Cx²+Jy'tuxy X y(2)21 use Rennoull EQ.

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Q: Inx+ 1 dy If y = then %3D 2x3 - 3x' will be dx (2x – 3x) + 1) – (In x + 1)(6x² – 3) А. (2x³ – 3x)² -…

A: Use the formula of differentiation of fraction of Two functions in same variable.

Q: 2 If the time. =1 moves in Such wery 1-12 + ²√2 = 1/², where c is a constmit, then 92 b Prove that…

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Q: (4х — 5у + 6)dx + (7x— 2у — 3) dy %3D0

A: Given that 4x-5y+6dx=7x-2y-3dy=0dydx=-4x-5y+67x-2y-3this form is equation reduciable to homogeneous…

Q: y(y2 + 1)dx + x(y2 – 1)dy = 0

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find P.S. of (16x +5y) dx + (3x+y) dy = 0 If the curre to pass thru the point (1,-3)

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: If y = (x+-) (2x – 3), then dy will be dx a (2x+) + (x = 3)(1 +) G++)(e - x2) + (; ++) = A. (2x +=)…

A: Given that                          y=x+1x2x-3

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: Q3. Find y= fx) such that y

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Q: 24. у (2х —у + 2) dx + 2(х — у) dy %3D0

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Q: y = 1+4. stretched horizontally by a factor of 3

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Q: use Lagrarge mul tipliers Sublect to the Constcair t to mekim,ze x+2y=5

A: Consider the given information. fx,y=x+4xy+6y and x+2y=5 Now, make the auxiliary function.…

Q: - choose the correct answer If y = t^2/(t^2+1) and t= v(2x+1) the = dyldx %3D 1/N(2x+1) O 2(x+1)^2 O…

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Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

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Q: u-3 15) If y= u+4 and u = 2/x+ 2, find when x = 7 dx %3D

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Q: BCSolve y" + 2y' + 2y = 8(t – n) with y(0) = y'(0) = 0 6.

A: Given differential equation is y''+2y'+2y=δ(t-π)    (1) with boundary condition y(0)=y'(0)=0  Let…

Q: If (2xy?+4) dx +2 (x*y-3) dy = 0 then ƏP/ay # ƏQ/ax *

A: Given: The equation is, 2xy2+4dx+2x2y-3dy=0 And ∂P∂y≠∂Q∂x To find: Whether it is true or false.…

Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: .3 S(3 – e3*)²dx

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Q: 7.Find a²z of z = 2x³-5xy² xy

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Q: 6) y' 2.x-3y+4 x+y+2

A: Answer

Q: Evaluate s's' √y³ +1 dy dx

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Q: 1) (2x - 3y + 4)dx + (3x – 2y + 1)dy = 0 c %3D

A: Given that, (2x-3y+4)dx+(3x-2y+1)dy=0. The equation is of the form Mdx=Ndy Now take My,Nx,…

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

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Q: 3. X is N(5,9). Obtain the pdf of Y=3X-5 and Z=5-X.

A: The X is N(5,9).Know that if X is normally distributed then the PDF of X isWant to calculate the PDF…

Q: 1. 2(2ay+ 4y – 3)dx + (x + 2)²dy = 0

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Q: ху (x+ Vy² + 1)dx – (y - dy = 0 2+1 4.

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Q: What is the image of (4,-1)(4,−1) after a reflection over the line y=xy=x?

A: Reflection over y=x means:  (x,y)→(y,x)  We need to find reflection of (4,-1) over y=x line .