Let r(t) = (t, 3 cos(t), 3sin(t))

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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Q: 8y'' - 12y' + 5y = 6 cos t

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Q: | cos zdr + sen ydy + x?dz

A: The solution are next step

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

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Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: Find y if: (a) y = (In x)cOs z (b) y = In(x² + y²> %3D

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Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

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Q: Let x (t) =y(t) +sin(t), x2(t)=y (t) then x2(t)= x,(t)- cos(t) Select one: O True False

A: given x1(t)=y(t)+sin(t) , x2(t)=y'(t)

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

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Q: Compute the Jacobian of : O(r, 0) = (9r cos 0, 4r sin 0)

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Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

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Q: 3. u, = u, - sin x cos t, 1 >0 В.С.: и(0, г) %3D0, = () 1.С.: «(х, 0) %3D 0, u,(x. 0) = 0

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Q: 2. Let f(r, y,z) = In(r² + 2) + ye* – cos(2yz). Find faya- COS

A: see below the answer as per bartleby guideline we have to solve the first question onl

Q: Let cos(t) sin(t)] t3 t² t4 t and B(t) = 2 [-sin(t) cos(t). Verify that (AB)'(t) = A' (t)B(t) +…

A: Given  At=costsint-sintcostBt=tt3t2t4 Now,  A't=cost-sintsintcostB't=tt2t3t4

Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: Graph the following vector fields

A: (a)known fact:

Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: 3. Why is u = cos x, dv = x dx a poor choice for evaluating | x cos x dx?

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Q: 18 Compute r''(t) when r(t) = (t°,9t, cos t). r'(t) = OID

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Q: 1 ezt dz 2ni Izl=2 z2+1 cos (t) o tan (t) o sec (t) o sin(t) o

A: See the attachment

Q: х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

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Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: Suppose A(t) = [ e^t 0 0 0 cos t sin t 0 −sin t cos t]…

A: Given: At=et000cos tsin t0-sin tcos t To Find: To show that At-1 exists and then to find it.

Q: Evaluates t cos(2t*) dt

A: here we will put 2t4 = u then solve further

Q: 3- h(x, y, z) = cos xy + e*y + In zx, Po (1,0,1/2), A = i + 2j + 2k

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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: 1. r(t) = ti + (In cos t)j, -T/2 < t < T/2

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Suppose that w = x² + y? + z², x = cos 0, y = sin 0, z = tan 6. Use the chain rule to find dw when 0…

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Q: 1) f(t) =t cos(@t) 2) f(t)=tsin(@t) 3) f(t) =t cosh(at)

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Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

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Q: Let C be defined by 7(t) = |cos (t), sin (2t), t²| for 0 < t < n 2 sin(Vz) 9x*dx + 2zdy + + 2y ) dz…

A: Using the result that  ∫cF·dr=∫cPdx+Qdy+Rdz=∫P(r→(t))dxdt+Q(r→(t))dydt+R(r→(t))dzdt dt Here,…

Q: 3. Given that z = e" cos (), u = 4e2" – sin 2y, v = e" + n tan r. COS - Use chain rule to find dz/ðx…

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Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: 3. If x = (sin t+cos t), y = (cos t-sin t), (1 < t < 4), evaluate ip, dt. dt dt

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Q: 2s Prove that L(t sin t) (s²+1)²

A: We can use the concept of Laplace transform in order to solve the given problem.

Q: If u = x3 + y3 where x = a cos t, y = b sin t, then du dt

A: Solution

Q: R. 4, = U, - sin x cos t, :>r > 0 B.C.: «(0, t) = 0, 1.C.: u(x, 0} = 0, 1,(x. 0) = 0

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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: Calculate $ |z|=1 z²e¹/z cos(1/z) dz.

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Q: If z=x+iy=r(cos(0) + isin(e))then

A: The given equation is z=x+iy=rcosθ+isinθ.

Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

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Q: Find the convolution of f(t)=cos(t)f(t)=cos(t) and g(t)=cos(2t)

A: Given function is f(t)=cos(t) and g(t)=cos(2t)

Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…

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Q: E(z, t) = ex cos(@t – kz + Þ1) + ey cos(wt – kz + $2) = €;E× +e,Ey %3D

A: Consider the given equation: Where,

Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: Let z=In(x²+y²) where x=ue"sin t and y = ue"cos t. If u=- 2 and 1=0 then is equal to %3D ....

A: Multivariable function: When a function f has more than one independent variable and only one…

Q: . Let z = x2 – x*y where x = r sin 0 and y = r cos 0. az and ae az Use the chain rule to find ar…

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