Q4/ a2w a2w Find and where w = sin(xy) cec(cos(x+y)) дх ду ду дх

Q: aw 1(dw If w = f (x,y) and x=r.cos0, y=r.sine Prove that - * = $² + fy² ar 2a0

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Q: (3t+t²)sin (2t)dt

A: We have to integrate the function        (3t + t2)sin(2t)

Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

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Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: Eliminate the arbitrary constant/s: y = C1e^ax cosbx + C2e^ax sinbx where a and b are parameters (…

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Q: Q3- Find i) S sin3x.cos(-5x)dx

A: We have to evaluate the following integral: int sin 3x . cos (-5x) dx

Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

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Q: Q. It sin x Cos X XCOS xQ /- sin xd 3.

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Q: 4 sin' t cos tdt 4 sin"(t) cos (t) %3D

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Q: Q1\ Differentiate the following (choose two only) 1)z = sin (3x + 1) 2)f (x) = 3cot-12t 3)y = e 8*…

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Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: ∫(3t+t²)sin⁡(2t)dt

A: Given that, the integral is ∫3t+t2sit2tdt.…

Q: Using Variation of Parameters 4y''+4=cos-1x

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Q: 4. J (cos x – sin x)²dx

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Q: S*r(sin³x cos x + sin x cos x) dx -- 4 Ja sin 50 de

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Q: Check by differentiation that y = 2 cos t + 6 sin t is a solution to y"+y= 0 by finding the terms in…

A: Here,  y=2cost+6sint

Q: T/2 cos t dt 1 + sin²t

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Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: Q.3) 3+4x+20 dx = a) Q.4) f sin5x sin4x dx = tan-(+) 4 a) = (cosx - cos9x 9 cos9x c) (cosx +°%$*) +…

A: ∫1x2+4x+20dx∫sin5xsin4xdx

Q: ý(t) + 100 y(t) = 15 cos 5t + 20 sin 5t, y(0) = 25, ý(t)= 0 V138388 [ y(t) = - Q1 = 2n – tan cos…

A: Given that y''(t)+100y(t)=15cos5t+20sin5t, y(0)=25,y(t)=0 Take the homogenous equation,…

Q: 3 dy Зу =-sin -1 2 - sin +C V4-9y2 3 A) True B) False

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Q: Q3.a) Find if y + SE rsecx -dt = xy sint+1 dz Q4.a) if z = sin²0, and 0 = w² + cos (w) find-

A: 3a):  y+∫xsecx11+sintdt=xydifferentiate both sides and use Leibniz rule for differentiating the…

Q: Classify and Solve; +9 = cos² t + sin² t + cosh t + sinh t + 3 sin t – 3t dt dt2

A: d2ydt2+9dydt=cos2t+sin2t+cosht+sinht+3sint-3t…

Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: Q: Classify and Solve dy sin x dx sin x sin 2x +y cos x

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Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (z²x + cosx*)] [4(cash2x-sinh2x)] (16)…

A: Given that, y(x)=∂2∂x∂zz2x+cosx44cosh2x-sinh2x16cos2πxddx(2x2) This can be rewritten as,…

Q: 4. f(t) = (e^(10t)) sin(2t) 5. f(t) = (e^(9t)) sinh(5t)

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Q: 2 f(t) = ( tv4t2 + 1, sin(t) cos² (t), t2 + 1

A: As you ask parts b and c. in part b we need to find the equation of the tangent line to the curve at…

Q: 4 + cos t -dt 1 – sin t

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Q: 7. Evaluate t' sin(2t“) dt .

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Q: 6) F Sin12y Cos’ y dy

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Q: 2T -TT Evaluate: S. (sin x + cos y)dx dy II SII 71I

A: Let give integral is equal to I

Q: Q2: Evaluate: * Jx* sin(1- x)dx?

A: use substitution method to solve the integral

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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Q: F(x, y) = 3x – 4y3 + 5x°ys + cos(x) – 3 sin?(y) |

A: Given query is to find the partial derivative onnf the expression.

Q: tegral 1 -r³e"la0 cos²e ,² dr sin@d0 ¢ do = x 32πα x = ? %3D

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Q: A ) Find ſ cos 5t dt B) If y = x² + , x = 2t -5 then find dt

A: A)-     I=∫Cos5t dtlet 5t=uderivating both sides5 dt = duSo,I=15∫Cos u du = 15 Sin u +C…

Q: x³ + y³ + 3 x² siny tan z = 5 az dz and əx Find ду

A: Given,          x3+y3+3x2sinytanz=5

Q: QIN Evaulate : f v2 + cos4t sin4t dt

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Q: 3 Find cos(x+y), given that cosx= and siny = 2 3 TT <y<2n. 0<x< 2 Select one: V5-2/15 a. 10 b. None…

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Q: 2 cosh V5t + t5 1 -2t sin 2t

A: Definition of Laplace transform :Let f(t) be a function Laplace transform of the function is…

Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: 1. Eliminate the parameter tgiven x = t – 3 sint and y = 2 + 3 cos t.

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Q: 3e7" sin(2y) 3e7 sin(2y) dy

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Q: Q2: (a) Evaluate ſ cosx sinx V1 – sin4x dx.

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Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: H.W. 1) Lt² sin wt 2)L t cos wt 3)L t² sin 4t 4) Lt³ cos wt .3

A: Recall the Laplace's Transformation, L{tnf(t)}=(-1)ndndsnL{f(t)} where L is LaplaceTherefore,…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: