® Use Craumoy's rule to solre fhe following linear syslems: rele to solve al fxy=0 8? S x+2y-2 = 0 12x-y+32=D0 (-2,2,2)

Q: U= at ² w + 0х2 8² w dy² where 61, 62, 63 are constants and b₁ +6₂ +63 " 8² w + = W. az² Item 8.pdf…

A: Topic:- application of partial derivatives

Q: 159. Evaluate integral O (x2 + y?) dæ + 2xydy, where C is the curve that follows parabola y = x²…

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Q: Prad of Padius s Ciscle to (a) E B-j)2+2)

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Q: 2. (a) Use Pythagoras' theorem to find the length of the line segment y = 2x from (1, 2) to (2, 4).…

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Q: dx Given: 7-ge-2x. Using u-substitution and transforming the integrand, find du. A 18e-2xdx B -…

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Q: Find div F and curl F if F(c, y, z) = 10e*Y i – 9 cos yj+ 4sin? z k. div F= curl F=

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Q: The linear approximation for f(x,y)=Vy+cos?(x) at (0,63) is O L(x.y)=(65+y) 16 L(x,V)=(65-y)

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Q: 5) y =f(x) impending , 8y2= x? -x4, t sxs= %3D %3D r3 Coleu lote the sufoce orea of the formed…

A: We are given that 8y2 = x2 - x4 and 1/√3 ≤ x ≤ 1/√2. We need to calculate the surface area of the…

Q: As water flows through a tube of radius R = 10 cm, the velocity v ofan individual water particle…

A: Given:  dv/dr = -0.06r, R = 10 cm To Find: v(r)

Q: U +2y at (0, 0) to estimate Use the linear approximation of f (x, y) = e3x²- f(-0.03, 0.03) =

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Q: What is the graph of r(t)=2 costi + sintj?

A: Vector-valued function : It is a function of the form  r(t)=f(t)i⏜+g(t)j⏜ or…

Q: (u, v) ~ (x, y) as (x, y) → (0,0) that will bring to the sum of squares z = A1u? + A2v² the…

A: given u=ux,yv=vx,y   and u,v~x,y as x,y→0,0 define a function z=λ1u2+λ2v2 where…

Q: folve using NP Laplace Tranform: y" -y': et corlt) x(0)=0, x'(0): 0

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Q: A Find a numbel z That satisfies The condubion g af The MUT I dx= 9 4 -4 O -a 0-15

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Q: The acceleration of a particle is given by a(t) = 6.0 m/s³ t. Find (a) v(t) and (b) x(t) for a…

A: a(t) = 6t m/s2 v0 = x0 = 0

Q: interior to a Ex: let to be any Simple closed Contour C, when flaxed ?? de no dz = 2πT ( Hw a) and…

A: Cauchy integral formula for higher order derivative is :-fn(z0)=n!2πi∫cf(z)(z-z0)n+1dzwhere c is a…

Q: give the acceleration a = d2s/dt2, initial velocity,and initial position of an object moving on a…

A: We know that, acceleration is rate of change of velocity a=dvdt and velocity is rate of change of…

Q: Now, evaluating / y(x² + y°)¯'dA, | y(x? + y²)¯'dA = -dA x² + y? r sin 0 -rdrde 5x sin Odrde sin…

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Q: Example: Given, y = 4cx .2 %3D Find orthogonal trajectores. Tikrit 1 Civil

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Q: Green's Theorem (8x – f,) dA = f dx + g dy %3D (Circulation form)

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Q: Find div F and curl F if F(x, y, z) = 9e"Y i – 2 cos yj+ 7 sin? z k. div F= curl F=

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Q: Adistance particle travels counterclockwise around a circle of 36m radius so that the from a fixed…

A: Solution: Consider the given position equation of the particle is s = 20 t + 2 t2 where t is the…

Q: (iii) The moment of inertia I of an annulus of inner radius 'a' outer radius 'b' and mass 'm' is…

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Q: Еxample : Evaluate S. (2xy – x²)dx + (x+ y²) dy such that c is a curve bounded by y? | — х, у3D х2 ?…

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Q: X is the midpoint of UV. Y is the midpoint of UW. If MZUXY = 60, find mZV. X V M. mZV=

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Q: dA When the radius r of a sphere increases with time t, the change in area is dt O a. dr 4a r dt O…

A: Surface Area of sphere = 4πr2  r= radius of sphere

Q: Test for an ext remum o f t he functional 1 [2? y² + x? y']dæ, y(0) = 0, y(1) = 1 0.

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Q: m25 = An° Inscribed Angle X= 110° 150 Tangent-Chord X= 2 Chords P. a·b=c d m° %3D Tangent-Secant 9.…

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Q: 5. Express the flowing quantities in rectangular form. a) sec( + j1) cot(17/12 + j3 cosh(2 + j3) b)…

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Q: Integrate the function H(x,y,z) = 2x2/37 – 12z over the parabolic dome z= 3- 3x - 3y2, z> 0. .... ||…

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Q: he Marcinal revenue ( MR)Cnd Marginal Cose funchen Of a gicen product MC= 50 to Find Tle tota recenu…

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Q: sove the focowing using Lagrange Multiptiers: Maximi ze flx, Y, 2) solaject to x2 + y + 22 =1 Ax +…

A: Method of Lagrange Multipliers : 1.) Solve the system of equations .…

Q: A partide moves along the x-axiİS, The velocity of the particle at time t is ot-t.A gřaph is given…

A: Given, The velocity of the particle at time t is vt=6t-t2

Q: Find div F and curl F if F(x, y, z) = 10e"Y i – cos yj+ 8 sin? z k. div F= curl F=

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Q: (x -2xyi)dz over the contour :z= t +it^2,0 t 1, where x = Re z, y = Im z evaluate

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Q: A particle moves in the xy plane so that at any time –2 <t< 2, x = 3 sin t and y =t – 4 cost + 1.…

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Q: Describe the motion of a particle with position (x, y) as t varies in the given interval.x =…

A: To find: The motion of particle.The expression is rewritten as,

Q: The coordinates of a particle moving in the metric ??−plane are differentiable functions of time ?…

A: We have, dxdt=10 m/sec , dydt=5 m/sec Let us consider that D is the distance from the origin, then…

Q: Find div F and curl F if F(x, y, z) = 7e*Y i – 6 cos yj+ 10 sin? z k. - div F= curl F=

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Q: locate the bifurcation values of α for the one-parameter family and describe the bifurcation that…

A: To locate the bifurcation values.

Q: Calculath hu. kngn of me parameme corcngh cun C of the Ungtin X(t) = 2cost -coszt y Ct) = 25int…

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Q: Find div F and curl F if F(x, y, z) = 3e"Y i – 6 cos yj+ 10 sin? z k. div F= curl F=

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Q: Evaluate fy and f, at the given point. f(x, y) = e³Y sin(x), (T, 0) fx(T, 0) fy(T, 0) %3D

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Q: F = xzi + xyzj - y?k, find i. V•F ii. V x F i. div(curl F)

A: Given F=xzi +xyz j-y2k        ∇=i ∂∂x+j∂∂y+k∂∂zi ∇.F=i ∂∂x+j∂∂y+k∂∂z.xzi+xyz+jy2k…

Q: yunction 912) di Continuous en a Contour c oy dength l, and A M be 1412) em C, then the dyppor hound…

A: Suppose that w (t) be a complex function that is piecewise continuous on the interval . Then .  Let…

Q: Elimin ate th e parameter from the param etric equations x = E, y = 4t +2;0 sts4.

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Q: O IPR= ( i+ ();+(SZ Int) k %3D is the positian vechor of aporticule in space defermine at tei W the…

A: given position vector is                                             R=21+ti+t33j+2lntk velocity…

Q: Answer this ASAP Find the integral of F(r).dr, if F(r(t)) = xy, x²y²] C is a curve of an equation of…

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Q: g(z) : nction defined on R by %3D 1+.Write ar ermine its domain. Explain your reasoning.

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