1 1 S [ sin(1+ y²)dydx= 1- cosl a. 2 cos 5

Q: 3. Solve: cos xdx + ( 1+ | sin ædy = 0 %3D

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Q: Solve the following initial value problem. y) = -3 sint+2 cos t with y"'(0)= 9, y"(0) = - 2, y'(0) =…

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Q: π/4 1 π/4 sin TX cos 2y sin 4z dy dx dz = 0 0 0 (Type an exact answer, using n as needed.)

A: Solution

Q: 1 Vx + 10 — о(х), х — 0 te-2n 10n В. о(1/п), п — о 1 — о(е "), п — sin æ = x- +0(x°), x → 0 3 D. n2…

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Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3*) 4. y = cos 2x (e*²-1)…

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Q: Find dy/dt. y (1 + sin 10t)-3 Select one: A. -3(1 + sin 10t)* B. -30(1 + sin 10t)¯“ cos 10t C.…

A: The solution is given below in the next step:

Q: y=Sin x -37 30 Ly= cos x - 37 -2 77 ST 377 2. HN - 15

A: Answer is mentioned below

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: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). What…

A: The position at time t ≥ 0 of a particle moving along a coordinate line is s = 10 cos(t + π/4) We…

Q: 1) Solve the IVP: y" + 2y' + 2y = 5 sin t + 5 cos t : y(0) = 1 and y'(0) = 2

A: Given initial value problem is  y''+2y'+2y=5sint+5cost, y(0)=1, y'(0)=2. Let y'=dydt=Dy and…

Q: Can i get help step by step with this problem?

A: Recall the following facts.

Q: 19 18. sin x cos x dx 1-3cos 2x dt 1+ e-t

A: The given integrals are;  19) sinxcosx/(1-3cos2x)  18)1/(1+e-t).

Q: Question 2 Find the differential dy: y= sin O dy E In a + sin( rVE dr Cos ( xY O (E) None of these…

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Q: Solve the following 1 √√1-3x siny Cos 2y +1 cb₁ x² y² + x³ In x = 1 - 3 xy (a) - dx + dy = 0

A: We have to solve the differential equations given as follows a) 1sin ydx+1-3xcos 2y+1dy=0b)…

Q: If k 0 then the trigonometric integral [ 3 sin³ (kx) dx is equal to ¹(3 cos(kr) cos³ (kr)] + C

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Q: Sf(x) dx = 1 0.694 (sin(x) dx = 1 0.694 COS TX T C = 2 C 0.694 How? ==→ 1-C05 (0.69471) = 1694 -

A: To determine the value of C .

Q: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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Q: (3+ 7cos (x)) sin? (x) de 28. 29. sin° (9y) sec² (9y) dy / tan" (2) cos" (2) dz 30. [tan(2t) – sin°…

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

Q: 012 (01 अति लघु उत्तरीय प्रश्न dy ज्ञात कीजिए- dx 1. ax +2hxy+ by = 0. 3. 2x+3y sin y. %3D 5. ax+ by…

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Q: 1. Find the following antiderivatives: (b) (cos(5e) - sin(21)) dt eat (c) -2t dt 2

A: As per guideline we have to solve only three

Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

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Q: -9 4s4+s*V5-6 ds s4 1-cos? x dx sin x 2. 3.

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Q: 1 The value of S dx at x=0 is sinx+cosx C V7 (Inv2+1) +c Cn|vZ+ 1] +c ㅇ글미VZ+ 1| + c c -공in(V2+ 1) +…

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Q: 5) S V2 + sin 3t · cos 3t dt

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Q: dx+ 1.5 +§ (5r – 15)cos (5х — 15)сos dx COS 1.5 Jo (5x)cos 1.5

A: We have to apply the integral by parts.

Q: Given In = S cos" x dx = - cos"-1 x sin x + In-2 ; %3D n/2 determine a reduction formula for cos" x…

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Q: 1 ao et/2 dt = 0.50 2 An e-1/2 cos 2nt dt = 0.504 1+ 16n? 8n b, = et/2 sin 2nt dt = 0.504

A: a0 = (1/π) ∫0π e-t/2 dt , put -t/2 = x , dt = - 2dx Using formula ∫ et dt = et + c a0 = (1/π) ∫ ex…

Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

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Q: 13. Find the differential dy for each of the following. a) y = cos 2x- sin 3x b) y = x2 – V36 – x² |…

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Q: Show that where n is a positive integer.

A: To show

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

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Q: 13. (2х + 1) sin 4x dx; и — 2х + 1, dv %3D sin 4x d 14. х cos 4x dx; и %3D х, dv 3D сos 4x dx

A: 13:      ∫(2x+1) sin4x dx                14:      ∫x cos4x dx

Q: A) /16 /2 cos (167 x5 ) dx dy. Os xs 2 Og ys x*

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Q: 7) Evaluate the indefinite integral / cos cos 2t sin 2t dt.

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Q: /16 cos (16л x5) dx dy. Os xs 2 Os ys x*

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Q: Find all solutions to 2 cos(0) = V3 on the interval 0 < 0 < 2n %3D 0 =

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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: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du

Q: Question 4) A* dy Q4) A: Compute dx at x=1 where y = xcos2x O cos3 cos1 cos2 No one of the previous

A: Given y=xcos2x

Q: 2. [ (1–3x)sin(}x)dx 4w dw 3. [* w°e™ dw w²e* -1

A: This question is taken from the definite integral in which we have to find the integral of the given…

Q: 1 Evaluate the equation /o x² sin (xy)dydx

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Q: cos (2t) 23. sin' (2t) dt 3

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Q: 1 find the value of so that ky"=-1 at y= For cos x- sin y=- O V3 2 4 4

A: Solution:-

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

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Q: 9 3 12 6 cos (x) SSS dx dy dz =| 0 0 4y (Type an exact answer.)

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Q: A particle moves such that its velocity at time t is given by: v = 3t2i + 2 cos(4t)j + t2k If its…

A: given velocity of the particle at time 't' v=3t2i+2cos4tj+t2k initial position x(0)=2i

Q: 10 - S sin(8a) arctan(sin 4x)da integralinin değeri aşağıdakilerden hangisidir? 9118002 8(T – 2) a)…

A: Given that  The integral  To evaluate the integral

Q: 1/10 1.A) e* cos(5x) dx integration by parts

A: Here we have to do integration by parts:   Apply integration by parts u as e3x and v = cos5x