Calculate , (2x + 7y) dx dy, where Dis the shaded region in the figure. x+ 2y = 10 6. 10 x+ 2y - 6 Hint: Use the map G(u, v) = (u – 2v, v). (Use decimal notation. Give your answer as a whole number.) L,(2x + 7y) dx dy=

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A: Given- fx,y=12x2y3 To find- ∫05fx,ydx and ∫05fx,ydy

Q: %3D %3D dz Find at (2, -2, 1) if x + y? +z2 = 6xz+6yz+21 = 5 =D1

A: Given equation : x2+y2+z2=6xz+6yz+21

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A:

Q: Let R be the region in the fourth quadrant bounded below by the parabola y=x²-3 and above by the…

A: Use double integral

Q: dz dz d For the function z= 4x° +7y+9xy, find dx' dy' ax2(-5, – 2), and dy 2(-5, - 2). dz

A: Consider the given function. z=4x3+7y2+9xy The objective of the problem is to find the partial…

Q: Calculate , (x + 8y) dx dy, where D is the shaded region in the figure. x+ 2y = 10 10 x+ 2y = 6…

A:

Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 7x, x= 6, Ax = 0.5 %3D %3D dy =…

A: Given y=x2-7x, x=6, dx=∆x ⇒dy=dydx·dx and ∆y=y(x+∆x)-y(x)

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A: Given:The chain rule of differentiation states that:Applying the derivative with respect to x and…

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A:

Q: Ir 9- ((2, y) | 2553,1SyS 3): D then: dz dy = %3D

A: Given D={(x,y)|2<=x<=3,1<=y<=3}

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A:

Q: Using the substitutions X = u+2, y=w+2; dx = du, dy= dw, the DE with linear coefficients (x + y-…

A: Using the substitutions X=u+2, y=w+2; dx = du, dy=dw, the DE with linear coefficients (x+y-4) dx +…

Q: "III. Vf dr = , where f = xy²z and Cis given by r (t) = (t +1, t², t³),0<t<2

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Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

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A:

Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

Q: 3) For the parametric system, find dy d2y When is the graph concave up or down? and dx dx2 x = t2 -…

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Q: dy I By writing u y", and using the chain rule, show that ) = ny- dx dx dy 2 Use the product rule to…

A: We have to find the derivative

Q: Find Dy, Dx and the value of x, y,z    x + y + z = 2   6x -4y+5z=31   5x +2y+2z=13

A:

Q: Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

A:

Q: y as a function of x. 2 y = u', u = 3v² + 3, v = %3D dy Find using the Chain Rule. dx dy dx

A: Given: y=u3          -&gt;Eq'n(1)            u=3v3+3   -&gt;Eq'n(2)           v=2x2…

Q: Transform the equation (2?y – 3y) y' + æy³ = 0 into a variable separable form - f (x) dx + g (y) dy…

A: The solution is given as

Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

A:

Q: Compute Δy and dy for the given values of x and Sketch a diagram showing the line segments with…

A: Given: Now,

Q: Find (ay), and (3x), ду ду X Əw = dv X (Simplify your answer.) at the point (w, x, y, z)=(1,-1,1,…

A:

Q: Find Vq if (a) =In (r) %3D (b) p= In (-) %3D We know r= /x² + y² + z2

A:

Q: dy =f'(g(x))g'(x). dx Given y = f(u) and u = g(x), find y= 6u +5, u=x* dx II

A: y=6u+5 ,  u=13x4 Here, fu=6u+5  &amp;  gx=13x4 Now, f/u=61+0  &amp;  g/x=134x3       ∵dxndx=nxn-1…

Q: Evaluate O xy dx + x°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3).

A: The solution is given by using greens theorem as follows

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A:

Q: /| 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y?…

A:

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: se dx af dw Find and dt ди Assume that w = f ( 8ts², ), -(х, у) — 5ху, and (x, y) = 7 ds dw ... dt…

A: Given : w=f8ts2 , 2st , ∂f∂xx,y=5xy , ∂f∂yx,y=x27To find : ∂w∂t , ∂w∂s Pre-requisite : Multivariable…

Q: Find fy, fy, and f, for f(x,y,z) = 4xy + 6xz + 2yz.

A: Given, f(x,y,z)=4xy+6xz+2yz

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A:

Q: Find the Jacobian d(x, y) / d(u, v) for the indicated change of variables. u- v), y =u + v) X = -

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Q: PART C dy 12. Show that dx 2 for the relation %3D V%3D10, x, y X. # 0. y

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Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

A:

Q: For f(x, y) = e3r +y, find Preview a. fr b. Jy Preview Preview c. f„(1, 1) = Preview d. f,(1, 1) =

A:

Q: dw Assume that w = f(s° +?) and f'(x) = e*. Find dw and ds dw at dw %3D ds II

A: We have, w = fs3+t2 f'(x) = ex To evaluate : Expression for ∂w∂t and ∂w∂s

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Q: If w = (y-z)(z-x)(x-y),find the value of dw , dw, dw +. Z-X +. dx dy dz

A: We have w=(y-z)(z-x)(x-y) dwdx=(y-z)[(z-x)(1)+(x-y)(-1)]        =(y-z)[(z-x-(x-y)]…

Q: find dw/dx, dw/dy, dw/dz using implicit differentation. Leave your answer in terms of x,y,z,and w.…

A: To find the implicit differentiation of the function: ln(2x2+y-z5+11w)=z...(1) So, take w as a…

Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

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A: We have to find

Q: 46. f(x. y) dx dy

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Q: Find 2 by using the Chain Rule with y as a composite of dx y = csc(u), u = x3 + 2. %3D

A: Given: y=csc( u) , u=x3+2  To find dydx

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A:

Q: f (u) and u = g(x), find dy/dx: a) y = cosu, u = -x/3 |

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

Q: 32. In the diagram, VW= 3, WX= 4, and VX= 8. Is WX tangent to OV? W b. yes a. no

A: We will use the property that radius is perpendicular to tangent line.