In Exercises 27–32, find dp/dq. q sin q 31. p = Ф — 1

Q: az Let z=xy-e'siny, x-uv, y=7Vu?+v?. Then at (u,v)=(7T,0) is du

A: Given that z=xy-exsiny, x=uv, y=7u2+v2find ∂z∂u at u,v=7π,0

Q: A particle is moving with the given data. Find theposition of the particle.  v (t ) = sin t - cos t…

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Q: 8. If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dtat t = 0?

A: Chain Rule d(f(g(x))dx   =   f'(g(x)) . g'(x) We have given r = sin(f(t))        f(0) =  π3  ,…

Q: (2) In Exercises c and d, find r, T, N, and B at the given value of t. d. r(t) = (cos t)i + (sin t)j…

A: Unit tangent vector , T(t) = r'(t)r'(t) Unit Normal vector , N(t ) = T'(t)T'(t) Unit Binormal vector…

Q: Find r' (t) where r(t) = (t sin t, t cos t, e"). O (cos t, – sin t, e2t) O (t cos t + sin t, sin t –…

A: We have to find derivative of the function: rt=tsint,tcost,e2t We know following rule for…

Q: a) +++ where C is the helix r(t) = cos(t) i + sin(t)j +t k, Osts2T

A: Note:- As per our guidelines, we can answer the first part of this problem as all the sub-parts are…

Q: 9 cos r+j9 sin 24 cos r+j24 sin + võ cos T+ jv6sin T+ V15 cos – j/15 sin T COS what would this be…

A: This is a problem of complex analysis.

Q: Po PDE: ar'r dr' ² do² 1 do 0 = do BCs: v, = dr at r=a v, = U„ cos 0 at r= 00 1 do Ve = -U„ sin 0 r…

A: The Laplace equation in polar coordinates for two dimension is given by, ∂2ϕ∂r2+1r∂ϕ∂r+1r2∂2ϕ∂θ2=0…

Q: 3- if you know that the wavefunction for a particle is given by Y = Aei(kxx-wt) Prove that the…

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Q: A particle moves with acceleration a(t) = 10 sin t + 3 cos t, s(0) = 1, v(0) = 2. Find s(t).

A: We have to find s(t)

Q: KIN T 2 2 6² 6³ 6² 0 0 ¢sinr do dr de

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Q: integral t 2 sin bt dt

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Q: C. If w=f(x,y) and x = r. cose, y=r. sine. Prove that aw ar aw +1 (2001) = fx² + fy²

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Q: a2u satisfies the wave equation əx² -n ə?u Verify that U(x, t) = e¬Vkt cos\TX k at2

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Q: If r (t) = (sin(t), cos(t), 2), then ſr (t) dt = 0.

A: The vector function is given by rt = sin(t),cos(t),2 To evaluate : ∫0πrtdt

Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

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Q: can you help me step by step please

A: Here the given function is s(t) and differentiates it with respect to t.

Q: The functions y,(t) = sin(2t), y,(t)= cos(2t) are linearly independent on (-0, x). Select one: OTrue…

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Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

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Q: r(t) = (tan(5t))i+t cos(t)j – Vtk

A: Given: rt=tan-15ti+tcostj-tk

Q: Exercise III (a) Let I = psin(ø) cos (0); y = p sin(6) sin(0); pcos(6). Then find the following. (i)…

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Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 4 + 3…

A: The solution is given below :

Q: In Exercises 51 and 52, find dy/dx at the given point. 51. (x + 2)? – 6(2y+ 3)2 = 3, (1, –1)

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Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3 + 3…

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Q: (b) Utt = t>0, u (r,0) = 3 sin r, u (r,0) = 0, 0 0.

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Q: au %3D ax at u(x, 0) = 0 ди (x, 0) = 0 at u(0, t) = sin? t u(1, г) — 0,

A: Given,           ∂2u∂t2-∂2u∂x2=0                       for 0&lt;x&lt;1, t&gt;0      ...(1)u(x,…

Q: 3) ft)= (t+リ sin (t+z)= t sinけtz) + sint +2) Asin(よ)+ - Cole) ds s Sin(2) +1- Gd ニ (8+1) - sind -…

A: We have to find the Laplace transformation of f(t).

Q: az Find when u = 0 and v dv 117 if z(x, y) = sin x + cos y, x = u •v, and y =u + v.

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Q: iven po r (t) = (sin (t), cos (t), In(cos (t))), (0, 1,0). T = 1 1 1 - N = V2 1 1 B = V2

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Q: (a) Evaluate where c is z = 1 %3D c cos(Tz)

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Q: d/dt [sec^3(t)] compute the derivate

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Q: yi + aj 2. Find the flux of F = across the curve C given by r(t) = a cos(t)i+a sin(t)j, ²+y² for 0…

A: ∵ Given thatF=-yi^+xj^x2+y2;           0≤t≤2π r(t)=acosti^+asintj^ As we know that Flux=∬ F·nds…

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

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Q: Find the lengths of the curves in Exercises 15 and 16.

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Q: (a) If f(x,y) = e" siny – e" sinx then verify that fry = fyz-

A: This question is related to partial derivatives.

Q: Fit a trigonometric function of the form f(t) = co +C sin(1) +cz cos(t) to the data points (0, 6),…

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Q: 65. The function z(u, v) = u cos v satisfies the equation dz cos U- ди sin v dz = 1. и до

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Q: . и., — и. — sin x сos t, t>0 В.С.: и(0, г) %3D0, 1.С.: и(х, 0) %3D 0, 1,(x. 0) = 0

A: Solution :-

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

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Q: L[t cos 2t

A: Please find the detailed solution in below images

Q: Q4 Find az when u = 0,v = 0 du If z = sin xy + xsiny, x = u2 + v² ,y = uv

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Q: Find the length of the cardioid r = 1 – cos 0.

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Q: 1 r(t) = (t sin t, (2t)³/2, t cos t), 0 < t < 2n. 3

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Q: (T/2 Q = [" 3 sin t(cos t)?dt

A: Given,        Q=∫0π23sintcost2dt

Q: Find the distance traveled by a particle with position (х, у); Cos t, y = (cos t)², 0 < t < 4TT X =

A: To solve this we have to use two point distance formula

Q: 4) Let [et e'sin(t) let e'cos(t) A(t) : Calculate |A(s) ds

A: Answer

Q: 11 z- CCW -dz, z2 - z de. c:|2- = sec(u), <ý<.cv Question 11) Find I =

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Q: 6. Let r = t sin t, y = t cos t, 0<t<1. dy (a) Find dr

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Q: Q: Show that the signal x(t) = sin(@ t) is a periodic signal.

A: →Any function x(t) is said to be periodic, when,…

Q: In Exercises 39-42, the velocity v(t) of a particle moving in the plane is given, along with the…

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