QUESTIONS what is v1- of the function t=r(cos e+ sin e cos b) in region (i) of the figure 2, (ii) 2.

Q: 9 y = Arctan(2+x 1-2x 10. x = cos't ; y = sin't

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Q: (cos x cos y cotx) dx - sin x sin y dy = 0. -

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Q: y sin(Vu +3u-1) Oy = Vx x+ vZx y = e* sec(tan(x*)) y%3D u = In cos(x? + 1)|

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Q: 3. sin x cos y dx + cos x sin y dy = 0

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Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: sin (x + y) %3D coS Xcos y 7. tan x + tany

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Q: sin t dy If y = tan" ), show that cos t-1 dt 2 II

A: Formula Sin2x + cos2x =1  Find dy/dt

Q: sin x sin y dx + cos x cos y dy = 0 2 mydx — пхdy

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Q: sin(x) sin(y)dx + cos(x) cos(y)dy = 0, y (0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: 4th order RK method  yi+1=yi +16k1+2k2+2k3+k4Where ti+1=tn+h          k1=fti,yi,…

Q: Determine dy/dx given that y = 1+sin x COS C 1 O (1+sin x)² -1 O 1+sin x 1 O 1+sin x -1 O (1+sin x)²

A: The objective of the question is determine the derivative of the given function and choose the…

Q: 3. + x° siny-y と3 cOS C fond C Frc foeと y g りな in) fy

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Q: 3. dy - 2** + e 2x cos (x) + Cos(x) y Fuctor8 Integrating

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Q: sin x dy Given: y = Compute for dx 1-2 cos x

A: The given function is y=sin x1-2 cos x

Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m − n)] dx…

A: Let's find.

Q: 2) Proof that If y = f(x) = = cos x then dx sin x

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Q: cOS X COsy dx + (1- sin x siny) dy of from X = 0 the urrve y sihx

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Q: e'sin" ) *sin sech (x-2) * sech (x-2) F (x) = Explain why g(z) - 0, is not differentialble at a2. if…

A: Here, fx=exsin3πxx2sechx-23

Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

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Q: 18. Find relative extrema off(x) = sin cos x, over the interval , I. Che where function is…

A: Consider the given function. fx=sinx2cosx Now, find the derivative of the function.…

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: sin(x) sin(y)dx + cos(x) cos(y)dy= 0, y(0) = 2, h = 0.5, Find y (1) using fourth-order RK

A: We have to find y(1) using fourth-order RK.

Q: (cos x cos y cotx) dx - sin x sin y dy = 0 -

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Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages When:x= 0;y =, %3D

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Q: ( 3cos³x-1 To evaluate the integrand can be transformed to 1- sin?x O [(3cosx - sec?x)dx o f3cosx (1…

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Q: sin 3x dr + 2y cos* 3x dy = 0 COS

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Q: Cos ly -A) %3D show that 2 ニ0 2 8x Sx8y

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Q: dy/dx=(x+siny)/(2y-xcosy) is an exact equation

A: Given that dydx=x+sinyy-xcosy we need to check that it an exact equation

Q: ope of the curve 2xy = In(e*) sin(x)

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Q: (sin y- y sin x)dx + (cosx + x cos y)dy = 0

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

Q: sin x sin y dx + cos x cos y dy = 0

A: Using variable separable method.

Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

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Q: 2. sin x siny dy + cos x cos y dx = x² sin x cos y dx

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Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: cos(x)y' + sin(x)y = 2cos (x) sin(x) – 1 G) = 3/2, 0 <x < 2 %3D 2)

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Q: In integrating the function f(3x + 5)(cos) dx using integration by parts, what would be your v? v =…

A: The integration by parts is done using the formula: ∫udv=uv-∫vdu. In general, the ILATE rule is used…

Q: solve eYsin(x) -y'cos"x = 0 2. cos¯x=0

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Q: e) cos (x + y) - cos(x - y) =-2sinxsiny

A: The LHS of the given equation is cosx+y-cosx-y. Note that, cosA+B=cosAcosB-sinAsinB and…

Q: Evaluate the integral. cost dt sin n² t - 5 sin t + 4 Select one:

A: We will substitute sint=x, then we will do partial fraction.

Q: cos(0)x – sin(0)y] sin(0)x + cos(0)Y T z || నా

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Q: (cos(2x) – sin(2x) cos(2x)) cos(x) – sin(x) For -dx%3D +C. What is F (x)?

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Q: b) x siny-ycos x- y = 1.

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Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

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Q: (sin x + cos x)dy + (cos x – sinx)dx = 0

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Q: [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]³ dx gettyimages When:x= 0; y = 2

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Q: 2. Integrate: a) Sx cos(x²) dx g) [3 cos(2nx) dx b) S tan³ x sec²x dx h) Se2% sin(e²*) dx c) S cot x…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: .3 cos(t) dt F(x)%3 cos(x). *

A: We are going to solve this question by the method of leibniz rule of differentiation under integral…

Q: ez - x - 1 lim 1-0 -1+cos r COS T

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