5 Jlgu ntinuity equation satisfied by u= 3x^2-2y^2, v=-6xy IO 4xy+y?, v= 6xy+ 3y .II O U = u=x-4y, v=y-4x .III O .34b JS Kåa/ "4b JS Ba" ġgà jäilg .Jlwjlg haal "Jlwg bàs" ggå jäil

Q: The TrapZoidalrule for fdx = 5 and Midpointrule %3D fex) olx = 4 what value does Simp Sans rule give…

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Q: tant dt 9,

A: To find the given integral ,use the substitution u=tan t .

Q: @ sinhz= loy (z+[2+1) %3D

A:

Q: Ju

A: To solve the Laplace equation for rectangular plate subject to the given boundary conditions.…

Q: 2. the inde fincte Integial X+8)(Vã-8) da

A: Just first the simplification of given integral and then integrate ∫xndx=xn+1n+1+C, where C is the…

Q: Solve 2 sinh(x)– cosh(x)= 5 by using the definition of the hyperbolic functions.

A: We know thatsinhθ=eθ-e-θ2coshθ=eθ+e-θ2

Q: Kim throws a ball against a wall at time t = 0. At time t = 1, it hits the wall and then at time t =…

A: The objective here is to check whether Mean Value Theorem can be applied to show that at some point…

Q: sech Vt tanh V dt Vi

A: Given : Intergral sech √t tanh √t dt / √t

Q: √xA)• dS over the surface of a hemispherical bowl of radius 2 and its circular rim if A = 3 sin(-)â,

A: Please see the attachment

Q: Differentiate y = arcsin (2r2) 4.r VI+ 4r4 Option 1 None of these VI- 44 Option 2 Option 3 4.

A: As we know that; The chain rule; fgx'=f'gx·g'x The Power Law; ddxxn=nxn-1 And ddxarcsin(x)=11-x2…

Q: 2. A particle moves along the parabola y = x in the first quadrant in such a way that its…

A: Given: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x -…

Q: Differentiate: y = 5 tan? (25z) %3D Oy = -750z tan (25z) sec (25r') Oy = -750z? tan (25z) sec (25z)…

A: We have to differentiate  y = 5 tan225x3.

Q: et secydx + sinydy = 0

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Q: the length of the curve y = coshx 1sx<2 is sinh(2) – sinh(1) Select one: O True O False

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: 3. S sec z tan z dz 2 2

A: Given: 3.∫sec23z tan23zdz

Q: 1. S(2cos4y – 1)i - sin4ydy

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: 6- y" + 4y = cot(t)

A: Given:        y''+4y=cott        4yt+d2dt2yt=cott The differential has the form        y''+py'+qy=s…

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: Ex: Siny dydx

A:

Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: 2 Find def differentiêt equatcn of: -I(082 Siny %3D

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Q: plot parucul Solu 1. y" +3y' – 4y= sin wx, 2. y" +3y' – 4y = cos wx.

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Q: sin(6y) sin(8y) dy.

A: Topic - integration

Q: arcsin 4y dy 1 – 16y2

A: Given: ∫arcsin4y1-16y2dy

Q: Solve (1+siny)dylx=[(2ycosy-(secy+tany)]dy.

A: This question is taken from a differential equation in which we have to solve the equation and take…

Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

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Q: ди ди x====u+Yay ?х

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Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

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Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

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Q: Differentiate: y = ln cosh (cos 2x) 3. O y = 6 sin 2x tanh(cos 2x) %3D O y = 6 sin 2x coth(cos 2x)…

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Q: The force on a particle is described by 5x³ – 5 at a point x along the x-axis. Find the work done in…

A:

Q: Intergrate:

A: To evaluate the integral.

Q: ex/Eveiluene the fallowing integrels 21/dx XInx

A: The given integrals are 1. ∫dxx1-x2. ∫dxx ln x

Q: A ball with mass 0.15kg is thrown upward with initial velocity 20m/sec from the roof of a building…

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Q: Q Find the time required for a cylinderical tank of radus 2.5 m and height 3 m to empty through a…

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Q: Evaluate the integral cot 2x dx cot2 2x - 15 -금사 csc 2x +C A Arcsec 4 B -In/cot 2x + cot? 2x – 15|+C…

A: Here, the given integral is: I=∫cot 2xcot22x-15dx

Q: expanded as odulus of x, the 1-e

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Q: Find y' where y = (tan(18z² +5)) / 18z3 +14 Answer: 54z2 O v' = sec2 (36z) /1823 + 14 + tan(182² +…

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Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

A:

Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: Express he equation n" = 4y in poar corinaes.

A: Given equation x2=4y

Q: ary differentia att=0 the ing

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Q: 3 ( tann cax) sech' cax) dx Iet v = +anh Cax) = 2 sech cax) dx dx = du 2 sech' cax ) u sech ca* ) du…

A: We  calculate it by using only  calculator. Where we put value of tan(6) as value of tanh(6) and…

Q: 2olue dy %3D

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Q: (7 – siny)y' = 3x2 + 2x

A:

Q: (a) Sizl=1 dz.

A: Here we use property of analytic function.

Q: suppose that the length of time between consecutive high tides is 12 hours and 26 mins. on a…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.