2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

Q: Find dz/ax andðz/@yif I z = x* sin(xy³).

A: If a function f(x, y) is to be partially differentiated with respect to x, then we treat the…

Q: The linear approximation at r = 0 to sin(2x) is A+ Bx where A is: and where B is:

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Q: Find the general solution of the following first-order ODE xy' = y + 2x3 sin?

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Q: -을 x e [T, 3 J Sinx =

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Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: b. Show that 0s cos ay dA s where R= (0. G ) sin Ax

A: This is a problem of double integration and inequality.

Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: Solve the D. E. to the I. V. P. sinx(e + 1)x'- cosx 1, y() = 0 O (1 + e') (1 + cos x) = 2 O (1 + e)…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x' – cosx = 1, y(0) = 0 COSX O In (1 + cos x) = 1 + e (1…

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Q: 2 sin(t) s(t) = et

A: Part (a) The displacement of the object is, s(t)=2sintet Integrate the expression with respect to t…

Q: find the pauticuler soluhion fr + loy = x'_e*sin(8x)

A: Solve particular integral in above differential equations.

Q: Eliminate the arbitrary constant/s of this equation to obtain the DE. Express the DE in general…

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Q: 2.f(t) = cosh wt sin wt

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: Given Lve f(t) dt = In(x) cos(x) + sin(3) :L.e- f(t) dt, find f(x). sin(3)

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Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: L[if i sin√2t dt²

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Q: Q1: If Z = x³ + y* + (x sin y) + (y cos x), Find Zx/Zy?

A: We are given: Z=x3+y4+(x sin y)+(y cos x)To find: ZxZy This can be calculated as follows:

Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: 220. Suppose f(x, y) = x + y, u = ex sin y, x = 1², and y = лt, where x = r cos and y = r sin 0.…

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Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: Express in the form x + jy (3) sin(t/4+j2)

A: Complex Number Question

Q: Q6A)If y = sin-¹ prove Zyy + 2 = 0

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Q: the Yp Vvnich OllOWing is a particu y" + 2y' + 5y = sin t where A; are constants determined by…

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Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: tan (e) 1+z* (d) (22+ cosh 2z)dz () z coshz dz zp-

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Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

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Q: (a) Find dr dy given that x²y + sin xy = 0.

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

Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

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Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

Q: 2.f (t) = cosh wt sin wt

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Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: Obtain the der a) cos(xy)=2y, find y'

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Q: * sin(Iny)dy is equal to y A -cos(ny) + C B none of these cos(Iny) + C y D cos((ny) + C cos(Iny) + C…

A: A standard integral in some cases can be converted to a standard integral with an appropriate…

Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: (f) If w=4x² +4y² +z² ,x= p sinø cos0, y= psinøsin0 , z =pcosø, Əw find and ap

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Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

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Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

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Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Q: (ii) Evaluate the integral. C/4 (sec t tan ti + t cos 2tj + sin? 2t cos 2tk) dt

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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,…

Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

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