? lim (z,y) (1,1) 2x – ry – y r2 – y2

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: w= Pcxiy,Z) = In (x+y+2) ,x= cost, and z = 4VE %3D 2X = y= Sint >use ch ain rule to Rind du in terms…

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Q: Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.

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Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: ∫∫R dydx; R={(x,y)l(0≤x≤1),[√(x)≤y≤√(4-3x)]}; R=limits

A: We will solve the following

Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…

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Q: Integrate counterclockwise dz by Cauchy's formula z2 – 16 counterclockwise around the circle C : |z…

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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: 28. Evaluate by Green's theorem (x - cosh y) dx + (y + sinx) dy, where C is the rectangle with…

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Q: Evaluate I 8z(2r? + y) cos(4.r* – y*)dzdy where R is the region above y 2r2, below y = -2r2, and…

A: We want to evaluate ∬R8x(2x2+y) cos(4x4-y2) dxdy over the region R, where R is region above y=2x2…

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: riable t. If 2sin (x)+4cos(y)=3a dy and dt 3, what is the val

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Q: 2s – 5t & y = 6s – 8t. %3D Let z(x, y) = x + 9y? where x = az дх ду да dy dz Calculate ds & and…

A: We use the chain rule

Q: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…

A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev

Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: dz (a) Use an appropriate form of the chain rule to find dx dz in terms of y in terms of x and if z…

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Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D

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

A: Solution:-

Q: D eter mine Paricular volution ( 2xy)dy = (y²-x²)dy j x=I,y= -2

A: In this question we have to determine the particular solution.

Q: dy _ 4xy+5y² can be transformed into a seperable DE The DE: dx xy +3x2 in x and z by using the…

A: The solution is given as

Q: 4хy + 5y? xy +3x? in x and z by using the substitution y = xz dy = can be transformed into a…

A: We will use the substitution to try to transform the given differential equation into separable…

Q: ) y = 3logst ) y deriv = (sech t) (1 - In(sech t

A: A function's derivative is the function whose value at x is f′. (x). The graph of a function's…

Q: dz Use chain rule to find at (u, v) = (1, 1) if dv z = z sin(y² – z + 1)4), e = 3u – v², y = vº.

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Q: a) Lollowng use Euler ncthoel tsoule The d = yx2-Y for メ=2 at h=o.Ś , h=0.25 y= x +zy h=ol y (2)= }

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Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: (d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y)…

A: Limit of a function: A function f is said to tend to a limit l as a point x, y tends to the point…

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

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Q: se Usa Grean's Thaoram to ecaloate the boundary of the region (travarsad cantarclodase) acadrant…

A: Given data-                   ∫c( ex + y2)dx +( ey + x2)dy. Where, e = Boundary of the region. We…

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates

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

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

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Q: 川- Q1 Verify that [(y² – 2x )dx +(2xy +x² )dy = [[] dA where C is the boundary of a regi ôy R R…

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Q: ry lim (z.v)¬(0,0) + y² exists.

A: Please refer the attached image for complete solution.

Q: dz at (u, v) = (1,1) if du Use chain rule to find -z + 1);), = x = 3u – v², y = u® z = x sin( (y? |…

A: If the input of the function is more than one, then it is called a multivariable function. In this…

Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

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

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Q: dz Use chain rule to find at (s, t) = (0, 1) if ds z = 6x + y² tan e – st, y = s² – ť. x = ebs

A: Consider a function of multivariable where and . Then according to the chain rule for…

Q: dy Use the formula dx Ay lim Ar¬0 Ax f(x + Ax) – f(x) lim Ax→0 %3D %3D Ax dy when y = dx 2 to find x…

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Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

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Q: E). f(x, y) = sen?(r2 – 0²) + In(r0 + 0), r = Vx2 + y² 0 = arctan con -

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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: X+Z+3Siny X +2y-2

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Q: 3.4.6 Evaluate the line integral [sin y dx + (x- cos y) dy] taken in the anticlockwise sense, where…

A: Green's Theorem States that  Let C be the positively oriented, smooth, and simple closed curve in a…

Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.