Show with e and 8 that lim (t2 – t – 1, t? – 2t – 2) = (5,6) t→-2

Q: Q2. If F = (x² - y² + 2xz)ī− (2xz − xy + yz)j + (z² + x²), find the divergence of curl F and curl of…

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Q: Evaluate the line integral 2 Cx2y)dx- 2xdy along each of the following closed paths, taken…

A: Given that the integral,

Q: Q7:- Find the limit of the following vector functions:- (1) Lim (t²i+ 2tj) (2) Lim(+1i, (3) Lim (ti…

A: We have to find the limit of the vector function.

Q: Show that each function in Exercise satisfies a Laplaceequation.ƒ(x, y) = e^-2ycos 2x

A: Given :

Q: By using the residue theorem, prove that 1 dx 4a3 where x E R, and a >0 is a parameter.

A: Given

Q: dw Use an appropriate form of the chain rule to find dt w = In(10x² – 4y + 5z³); c = t', y = tỉ, z =…

A: From the given function: w=ln10x2-4y+5z3 ; x=t12 ; y=t23 ; z=t-2 As we know that: The Power law:…

Q: Q1) Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

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Q: 3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) =…

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Q: If f: (a,b]-R has a local minimum at pe (a,b) and f is differentiable at p, then prove that f'(p) =…

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Q: t² + 1 t 1 %3D lim→1- h(t) = ?

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Q: Use the Chain Rule to find ôz/ðs and ôz/ôt. z = tan(u/v), u = 9s + 8t, v = 8s – 9t as az at

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Q: Compute I = (2x²132²y+ 4xy)ax +(x'+2x²-y') dy+zdz along The curve C C4U Cz UG given in the figure…

A: Given To compute I=∫C2x3+3x2y+4xy.dx+x3+2x2-y2dy+zdz along the curve C=C1∪C2∪C3 given in the figure.

Q: Q2. If F = (x² − y² + 2xz)ī − (2xz − xy + yz)j + (z² + x²)k, find the of curl F and curl of curl F…

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Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: Use the Chain Rule to find dz/əs and dz/at. z = tan(u/v), u = 8s + 3t, V = 3s 8t az as az Ət II

A: Given data: *z=tan(uv) *u=8s+3t and v=3s-8t The partial derivative of z with respect to s is given…

Q: Suppose z x'y' where x-st and y -t -s. Use the chain rule to determine as and a) -2xy't-4yx's;-…

A: The given multivariable function is: z=x2y2 ,       where x=st     and     y=t2-s2

Q: (6) Find the integral of the function piecewise linear path from (1,1) to (2,2) to (0,2). b) 22.3…

A: Given the function Fx,y=ey-x,e2x

Q: If y(t) solves the IVP dy = y2021 y2019 y(2021)= -2019, dt then lim y(t) is: t- 00 Oa. 1 O b. 00 O.O…

A: Given differential equation is dydt=y2021-y2019.       ........1 It is an autonomous differential…

Q: Calculate the divergence of cach of the following functions (a) r²î + y²§ + 2²k. (b) yzî + xzj+ xyk.…

A: As per the instruction, we will answer only the first 3 subparts. For (a), For a given vector fx, y,…

Q: H.w, considev The SyoLem by and Gass Jorolan limnat 8x-23+3=25 メ+33-2るー12 uメー5y - 3)

A: we have to find the solution of the system by Gauss - Jordan method.

Q: 27. Consider the piecewise path which goes along (t,3 – 3t, -t) for 0 <t<1, then along (1,t,-1+ t)…

A: Line Integral along the given parametric curve.

Q: Construct (a) slope field for the DE: y'+4 y'=x (b) tabulate the values at these 5 points ( 0,0 )(…

A: We have to sketch the slope field for the differential equation y'=x2-4y2. Then we  will tabulate…

Q: | Let u = x*y + y°23 where x = rse', y = rs²e=t, = 2, 8 = 1 and t = 0, by using Chain Rule. p2 Sint.…

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Q: B. Use Green's theorem to evaluate f (x²y)dx + y²dy Where C is close path formed y = x and y = x³…

A: Above first question is solved. Solving more than one question is against the policy of bartleby.

Q: dz a²z and 1 a) Find- Usin chain rule. If z = e*y – Sin xy, x=-, y=t? дх ду dt

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Q: Exercise Pustlems# . A. Determine the Yp of tue difft'l eghs shoun below 1) y"_ ay't ay = eCosx-…

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Q: - Emluste ihe given limt ké", ut, 177 2. Compute 1he dovivadv'e A she given vactor hu. F()-…

A: Since you have posted 3 questions here, i can answer only first one. Please reupload remaining…

Q: -5) as golve: x'= -3x + 3y +z -1 (**) x-sy-32 +7 2'=-3x + 74 +32-7 =) i) Does (**) have a solution…

A: As per norms, we will be solving only one question. If you need an answer to others then kindly…

Q: Let z = f(x, y) where g = e° cos t and y = e sin t. Use the Chain Rule to show: az, a z = e

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Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

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Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT>XT. Y T

A: Given a diagram: ZY=ZX To  prove YT&gt;XT

Q: 3) Find the divergence and curl of f3xi+ 5x} j + 2y²k, at the point (1,2,3)

A: Solution is done in step 2

Q: Consider the following. w = xyz, x = s + 5t, y = s – 5t, z = st? (a) Find aw/as and ôw/at by using…

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Q: If z = f(x,y) = tan x =t cose and y =t sin@. Use the Chain Rule method to find y as functions of t…

A: Given that z=f(x,y)=tan-1xy Where x=tcosθ,y=tsinθ Substituting, the values,…

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: 2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute…

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Q: Suppose F(x,y)=(4x+6y)i +(6x+4y)j. Evaluate the line integral for each of the given paths, which are…

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Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

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Q: Suppose z = x² sin y, x = -s² – 21² , y = 8st. dz A. Use the chain rule to find and * as functions…

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Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…

Q: Let z = f(x, y) where g = e° cos t and y = e° sin t. Use the Chain Rule to show: z = e

A: Let z = f(x, y) where x = es cos t and y = es  sin t. We will be using the chain rule to show,…

Q: Use the Chain Rule to find ôz/ds and ôz/ðt. z = tan(u/v), u = 5s + 9t, V = 9s – 5t az as az at

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Q: (a) z = 1– In y (b) 22 = 1. Show the traces as well.

A: Given a) z=1-ln(y) b) x29+y24+z2=1

Q: Use the chain rule to find ∂w/∂t given w =√ x^2 + y^2 + z^2 and x = cos(st), y = −2s ln(t) and z = s…

A: Solution:Given      w=x2+y2+z2x = cos(st), y = −2s ln(t) and z = s − 3t.To find…