Find TN and B for the carve at the indicated pont r(() = (t,t,e') at (0,0,1) T= B= ?

Q: If C is the line segment from (6, 1) to, (0,0), find the value of the line integral: S(5y i+ x) • dr…

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Q: Find Oz/ou and oz/ov for z=4e* ln(y), x=ln(u cos(v)), y = usin(v) at the point (u, v)=(2.7/4).

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Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

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Q: Show that the volume of solid formed by revolving one loop of the curve r2 = a? cos20 about the line…

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Q: If u = x? + y? + z?, where x = e2t, y = e2t cos (3t), z = e2t sin (3t), %3D du at t= 0 is dt then

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Q: az and dz Use the chain rule to find as at sin(0) r = st, 0 = s9 + t° %3D as az at

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Q: Find a. Əw dx a. aw əx and b. y (2π,1,-π) Əw at the point (x,y,z) = (2π, 1₁ - π) if w = x² + y² + z²…

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Q: 4) Solve the followingIVPusing LaplaceTransform. y′′−6y′+15y=2sin(3t)    ,y(0)=−1,y′(0)=−4

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Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: A=LDU where D-) then the humber of special solubion s bo Ax =0 is equal a-1/b.e/c.2/d.camt be deubie…

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

Q: A particle was following the trajectory r(t) = (e', sin (2t), t), but it starts flying tangentially…

A: SolutionGivenA particle was following the trajectory r(t)= (et,sin(2t),t) , but it starts flying…

Q: Compute yarctar y? = 1 – 1+ y? ctan(y)dy. Hint: Note that 1+ y? fractan(g)dy- +C

A: we have to comloute the integral ∫ y tan-1 (y) dy we solve this integral by integration by parts…

Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

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Q: Given: vector-valued function Ř(t) = (3 cos 2t, 9t, −3 sin 2t) 1. Reparametrize R using the directed…

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Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: Use Laplace Tranformation to solve the IVP.  y'+y=tsint  y(0)=0

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Q: Show that the general solution to the two-dimensional Laplace's Equation. et = 0 is (Acosh(tx)…

A: We have to show that the general solution to the two-dimensional Laplace's Equation…

Q: If C is the line segment from (1,3) to, (0, 0), find the value of the line integral: S(3y² i +3x}) ·…

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Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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

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Q: Determine the linearity and solve for the general solution to the given DE dx = ecos y dy х cot y

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Q: Solve the Laplace equation for a rectangular plate subject to the fol- lowing boundary conditions

A: Given: To solve the given Laplace equation for a rectangle plate subjected to the following boundary…

Q: Given YZ tangent to OJ at point Y, and mzWYX=104, what is mW XY? W

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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: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

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Q: sec 0 sec 0 - cos 0 -de

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Q: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

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Q: Given z=3 In(t) and y=9t² then find dy de dy da %3D

A: We use parametric differentiation

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: Use the Chain Rule to find dz/dt.z = sqt(8+x^2+y^2,    x = 4 ln t,    y = cos t dz/dt=

A: Please refer to the image below

Q: If u=lx+my and v=mx-ly,show that 1? + m? ди ди 1 + m?

A: Given  u = lx + my v = mx - ly

Q: dy 3. da + y = 2xy?e"

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Q: 1. Draw a sketch of the cylinder z= ==V36 – 4y2.

A: Given: z=1336-4y2

Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

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Q: Given z 15 In(t) and y= 225 t then find dy da dy dr?

A: Given that: x=15ln ty=225 t2

Q: The value of the line integral S(2xy²dx + 2a?ydy + dz) along a path joining the origin and the point…

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Q: A rod with density p(x)=4+sin(x) (in grams per cm) lies on the x-axis between x=0 and x=pi/3. Find…

A: Please see the explanation below

Q: find the valume 9tntrat ed by y= X? on [0,31 rotating abaut thlina X-5.(shell melthod) rated

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Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.

Q: A) The position of a particle P(x, y) at time t is given by: x= (2t + 3)i , y =+t.Find the distance…

A: Given:  position of particle is P(x,y) : x= 1/3(2t+3)^(3/2) y= t^2/2 +t

Q: Use methed of Cardinates to Solve PDE du t 37gu = o (32² +81y -3y) for V 64) E R for Y te B with the…

A: We will use the approach of the method you mentioned.

Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

A: Given that dydt=yβ-αy and y=y0 at t=0 We have to find the solution of the above equation.