In+1 Σ S. 3 5 n=1 Vn° +1 8. 8.

Q: ds 53. dt = 8 sin" (+ + 12). s (0) = 8

A: Given : dsdt=8sin2(t+π12)s(0)=8 Solve the initial value problem multiply both sides by dt then…

Q: need help with attached, thanks

A: Given function and interval are,

Q: (b) у" — 2у + у 3 еt sin(z)

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Q: Q2: Evaluate Seas cos²(y s) ds. إضافة ملف

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Q: I. Solve the heat o at with lot) - (2,t) 3TX 8TX aud Ulxio) = lo + 5 Cos - 3 Cos *

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Q: The value of 6 dz,where C:|z|= counterclockwise, is sinh(z+2) 7-4 O a. O b. 27isinh(3) sinh(3) O d.…

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Q: дz əs дz at || 11 z = e cos(8), r = st, 8 8 = √ S6 + 56

A: Solution is done in step 2,3

Q: r(t) =(sin 3t, cos 31, V7t), 1. Let a) Find T(t) and N(t)

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Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

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Q: if(r, y) = e sin 8y, then fry is given by: 2z O 16 e* sin 8y O – 16 e2* sin 8y O 16 e2 cos 8y O – 16…

A: Solving differential equations . To solve the differential equations.

Q: Find a solution u(x,t) to the problem ôu ôt = 1.71 a^2u/ðx^2, u(x, 0) = sin ( nx/2)+ 3 sin (…

A: We have to find the solution u(x, t) for the given problem.

Q: Given z = 2 cos t + 26 and y = 5 sin? t dz dy dy dz

A: Derivative of function in parametric form

Q: Which of the following is the form of a particular solution of y" +4y' = 3e2t + cos 2t + t? %3D

A: We have to find the particular solution of given diff equation.

Q: 0.6 e da, using Simpson's by taking EaN=6

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Q: b. y = -In (12yx²) + sin(y)e312xy + e12yx4

A: Given:

Q: 0 = 1 TT if m + n 68. sin mx sin nx dx if m n

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Q: A coil of inductance of 3H and a resistance of 200 is connected with an emf E =220sin3ot, where t is…

A: We will find out the required value.

Q: 7 26. У V2 + cos?t dt %3D

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Q: b) O cos(T n) T 1 00 (-1)" c) O 57 Tn 1 d) O nin (n + 2) T 1

A: Divergence test; Iflimn→∞ an≠0 then the series ∑n=1∞ an diverges.

Q: e+e¯ (a) Find all the solutions of cosh z 4 (Hint: cosh z 2

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: iP fca)ex+s and gixjex?-3- find the folllowiny D Rc fext

A: a)         f(f(x))=f(x+5)           =x+5+5           =x+10

Q: A) S sin edo b)S sec edo )Side Ssec?eddo E)S cos ede

A: We have to find the integral

Q: dv/du = (uv)² — 2(u — v) — 2.

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Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: and its solution EE{ Jm(VAmr) |amncos mô cos( /amict) m=Oh=1 и(r, 0, t) %3 + bmncos m0 sin(VAmict) +…

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Q: et sin t? blas Y - et cos t? lio -n/2 <t < 0

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Q: d 5. Prove (arccot(x)) dx -1 Be sure to provide a written justification for your work. 1+ x?

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Q: Solve the following Bernoulli's D.E.: dy +y%3D dr+y =x²y² dx

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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: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: Curves on surfaces Verify that the curve r(t) lies on the given surface. Give the name of the…

A: Definition used-               If curve r(t) lies on the given surface then r(t) should satisfy…

Q: S(z, y, 2) = 122 y sin(z) – Vy- z cos(r+y) 8PR Find Vf.

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Q: 7x +3 r sin r 5. If w then what is dw/dr?

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Q: - s = t? – sec t + 1 s

A: Given : s = t2-sect+1

Q: 1+ cos(t) 1 – sin(t) 2t) (n) y(t): (o) y(t) = In(5tª + 3t2 + 1) (p) y(t) = t° + T' + e™

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Q: dø +3ø = sin ot on (0,+∞) dt [$(0) = 1.

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Q: Given r 2 cos t+3 and y = 2 sin? t dr dt dy dt dy dr 13D

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Q: Given that u(t) = (e",5,cos 5t) and v(t) = (3,sin 41,4). Find [u(1) v()]. dt

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Q: S™ sin dt Sa" 2 1 b. 2 С. 3 d. None of the above a.

A: Given that, I=∫02πsint2dt we have to find the value of given integration.

Q: 2 (cos Fe tisin) - fsih 똥) Q) put Vz (cos 3+P sin I) 6. in expoitial hor m

A:

Q: - 2 sin(v) cos(v) – 4 Let h(v) = d Determine dv d dv

A: hv=-2sinvcosv-4

Q: Which of the following is the form of a particular solution of y" +4y' = 3e2t + cos 2t + t? Ae2" +…

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Q: -41 sin tZ dz, c: 1Z-il=2 z4 ans: 3. coshz dz ,C: IZ1=1 27T ans :

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Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

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Q: Solve the following Bernoulli DE's. ds 3(1+t?) 2ts(s³ – 1) dt

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Q: Solve the Following di Feerenti al equations a) 2ydy = (u?+1) de b) dy n2 y2 = n 2 %3D 6)(H2+1い) =…

A: We need to solve the given differential equations:a) 2ydy=x2+1dxb)dydx-x2y2=x2c)4x2+16dydx=cosycoty,…

Q: (5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L…

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Q: If So S, (x² + y² ) sin(x)dxdy= f L (2²² + y?) sin(x) dydæ a , then a, b are

A: Solution is below.

Q: 2. The speed of a particle at an arbitrary time t is given by || V(4t - 1) +sin? rt. Then V.d at t =…

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Q: If r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

A: