1. x = t, y = 1/(1 +²), z = t² 2. x = cos 4t, y = t, z = sin 4t 3. x = t? – 2, y = t³, z = tª + 1 4. x = sin 3t cos t, y = sin 3t sin t, z = t 5. x = cos t, y = sin t, z = In t 6. x = cos t, y = sin t, z = sin 5t A В E F

Q: If 1 =- V(x2 + y²) [(xyz – 3xy)a, + (zy² + 3x² )a, + xy az] And B = r² a, + sin 0 aø Find JÃ x B| at…

A: At P1, 2, 3, A→=25ax+195ay+25az. As r=x2+y2+z2, θ=tan-1x2+y2z and ϕ=tan-1yx, at the given point we…

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

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Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

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Q: If 7=(x+1)√√x² + yi+tan (3x-y)j and g = y find: fxcurl g+(g.V) at (0,1,1) x + y In(xy+2)+ i+…

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Q: 1. Given that x = 3 cos nt, y = 3 sin at and z = 4nt with 0<t<1. Evaluate (x + z) ds.

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Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: -3+ Sin zt dt 7 8-1 i uct-1) } e-zt 9- to

A: As per our guidelines I am solving only 1st for others kindly resubmit the question mentioning that…

Q: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

A: We have to find the derivative

Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

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Q: 21 40 JJJ. 7yz cos(10x5) dv, where E = sin (2) X = {(x, y, z) | 0 ≤ x ≤ 1,0 ≤ y ≤ x, x ≤ z ≤ 2x}

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Q: IER, t> 0, u(x,0) sin(87r) cos(90z). u + ru, =x

A: Solve partial differential equation by Lagrange method. Rewriting partial differential equation…

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: find 19. || xy cos y dA, R: -1 < x < 1, 0< y<T 20. y sin (x + y) dA, R: -T < x < 0, 0 < y < 21. et-y…

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Q: Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA –…

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Q: 4. a. Find zx + Zy: given that z(x, y) = tan(x3-3x?y2+2y4) V9-х2-у? b. If u then show that x ди дх…

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Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: Find dy/dt. 11) y = (ecost/9)4 A) cos e4 cos(t/9) B) sin e3 cos(t/9) e4 cos(t/9) D) - (esin(/9)3

A: Use the chain rule of derivative and simplify.

Q: The solution of the nonhomogeneous DE y" + y = sec?x is O None of these y = c1cosx + c2sinx +…

A: The given DE is, of the second-order and it is y''+y=sec2x which is non-homogeneous DE. So, first we…

Q: In Exercises 1–8, find the curve’s unit tangent vector. Also, find the length of the indicated…

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

Q: V, = {2i} m/s V, = {0.448v½i + 0.894v,j} m/s = {5 cos 0 i + 5 sin 0 j} m/s %3D 目。 Vb/r v, = 2 m/s 5…

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Q: 3. Let V = e cos(qr), with p = x ln(xyz), q = z cos(лy) and r = 2 tan−¹(y). ᎧᏙ By using the chain…

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Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: Given, y = (1+ cos 2t)-Find dy dt 8 sin 2t (1+cos 2t) sin 2t 5 (1+cos 2t) -4 sin 2t 5 (1+cos 2t) 8…

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Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

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Q: rION 4. Find du/dt for the following: 35. u = tan-(xy) ;x = sin t;y = sect x-y 36. и 3D In ;x = sec…

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Q: 2. The antiderivative of cos Π.Χ. A. -cos 2 B. KIN COS C. sin D. sin π.χ. is

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Q: Consider the following. x' = 4x + y y' = −2x + 2y,   X(0) = (−1, 2) The general solution is (x(t),…

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Q: 4. Evaluate the iterated integral T, cos(³) dydx. a. (cos 1- 1) b. 1 e. (sin 1- 1) f. 1 (1- cos 1)…

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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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: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: 1. Compute the following double in- 2. C tegrals. tegr a. STr 2.x + 4y + 10xy dA, R : 0 < x < 1,0 <…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: For the IVP: (1-4) cos ty"-In(r-1)y+VT+5y=e, y(2) =1, y(2) = 1

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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: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: If y = x² + sin(xy) find y' 2x+y cos ry 2y-x cos ry 2x+x cos ry y-æsiny 2x+y x cos ry x-y sin æ 2y…

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Q: Suppose z = tan x = u cos(5v) , and y = u sin(5v) . Compute dz/du and az/dv in two different ways:…

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Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

Q: 17. (D+ + 2Dz + 1)y = 5– 3x2 a. y = (C, + Czx) cos x + (C3 + C4) sin x – 3x2 + 17 b.y = (C1 + Czx)…

A: As per the company's guidelines we are supposed to solve first question for you, kindly repost other…

Q: If z = x2 – y2 and x = t cos 2r and y = r sin t , then a²z is (A) 2 cos?(2r) + 2r² cos²(t) – 2ry sin…

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Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: If 7 = (x+1)√√x² + yi+tan ¹(3x-y)j and g = = y find: fxcurl g+(g.V) at (0,1.4) x + y In(xy +2…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Q: 0.5 COS T - In(4 sin z) dz. J0.1

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Q: 00 L{cos}(s) = -st e cos(at) dt u cos(at) dv e^(-st)dt du = -asin(at)du v =| (-1/s)e^(-st) 00…

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