Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

Q: Find the steady-state current in the RLC-circuit in Fig. 71 when R = 50 2, L = 30 H, C = 0.025 F, E…

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Q: Use this result and the chain rule to find (Isinx|) pr all x € (-T, T),x + 0. dx

A: Given,           ddxsinxWe know that,             The derivative of absolute function is given by…

Q: How do you solve this problem?

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Q: tan (X) where : Let z=f(x,y) = (10 + 23x)y" where : 13 - e (t – 1) + tan'(t) , and y= (2- t) e'-…

A: Here, the given functions are: z=f(x,y)=(10+23x)ytan xx=13-e2e(t-1)+tan-1(t)y=(2-t)et-13(t-1)

Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: 2(+-3) cos (t-3) y ct) : Sin 2t cos 34

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Q: Use the differential operators y'"-5y'+6y=e* %3D

A: Given that a second order non homogeneous differential equation and find its solution. Here i…

Q: 7x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and

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Q: *) Use the Wronskian to determine whether the functions y₁ = sin(3x) and y₂ = cos(4x) cos(4x) are…

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Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

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Q: Give the Laplace transform of the solution to y' + 3y-4 e* – 2 sin(2 x), y(0)=5]

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Q: 10. Show that the function f(x, y) = e-2y cos 2x satisfies the Laplace equation.

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Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: Express dw/dt as a function of t by using the Chain Rule. Use the sum rule and split the bracket.…

Q: 1-t2 is 1+t2 The differential of u= In,

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Suppose z = x² sin y, x = 2s2 + 3t2, y = 4st. dz and A. Use the chain rule to find ds as functions…

A: Given: z=x2siny x=2s2+3t2 y=4st To find: Using chain rule, ∂z∂s and ∂z∂t ∂z∂s1,-2 and ∂z∂t1,-2

Q: Use Laplace transforms to solve the initial-value problem. x'' + 4x = cos t;   x(0)=0, x'(0)=0

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Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

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Q: 7-10 Use an appropriate form of the chain rule to find dw/dt. w = 5 cos xy - sin xz; x = 1/t, y = t,…

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Q: Express aw/ar and ôw/as as functions of r ands using chain rule w = = In(x² + y² + z²), x = res sinr…

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Q: Specify c-1, Co, Ci and p such that the formula c_1u(x – k) + cou(r) +cu(z+ k) u'(2) 2 denotes the…

A: This is a problem of Numerical Analysis.

Q: 1. Determine whether the functions f1(x) = cos 3x, f2(x) = x, and f3(x) = cos² x are linearly…

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Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

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Q: (a) express dw/ dt as a function of t, both by usingthe Chain Rule and by expressing w in terms of t…

A: w=x2+y2, x=cost, y=sint, t=π, We have to a) express dWdt as a function of t, both by using the Chain…

Q: 10. Show that the function f(r, y, 2) =e+ cos 5z satisfies the Laplace equation

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Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: We find dw/dt using chain rule. Here plug x = cos t, y = sin t, z = 4sqrt(t) and simplify.

Q: Determine if the following functions are linearly dependent or independent by determining their…

A: The Wronskian of a set of function y1, y2, y3 is defined as, If the Wronskian W is non-zero then…

Q: e) Suppose that W= √√x² + y² + z², x= cos 0, y = sin 0, z = tan 0. dw T Use the chain rule to find…

A: According to our company's guidelines I can only answer (e), since (e) and (f) are not inter…

Q: ди and ди ди Q3. If u = e"" sin p, p= sin x, q = z' In y, r=1/z, use chain rule to find

A: Find your answer below

Q: 19. Let f(x, y, z) = + sin(3z) + e"-2". Find the rate at which f is changing at (2, 4,0) in the…

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Q: 10. Show that the function f(x, y,z) = 2z³ – 3z(x² + y²) satisfies the Laplace Equation,

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Q: 1. Verify the initial value theorem for the voltage functions: a. 4+2 cos(t) b. t - cos (3t) and…

A: Given functions are a 4+2costb t-cos3t

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

A: ddxsinnx =cosnxddxnx =ncosnx

Q: Find a linear differential operator that annihilate the given function a) y=7e2x b) y=x+3xe6x

A: We know that gD is annihilator of y if gDy=0 (a) y=7e2x Differentiating wrt x, Dy=7×2e2x, D=ddx is…

Q: Let f1(x, y) - e cos(5y), f2(x, y) = x² – 25 y². Find Vf, and Vf2, and show that %3D (fv) = 0 for…

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Q: Q1) suppose that W= x2+y2+z² and x cos 0, y = sin0, z = tan 0 ,use the chain rule to find de when 0

A: We have, W=x2+y2+z2 and x=cosθ, y=sinθ, z=tanθ  We have to find, dwdθ=? at θ=π4

Q: Identify ALL linear differential equations. + (sin(t) + e' + 5x) + x = 0 d13 d²x + (1+t²) x = 10t…

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Q: Use the Laplace transform to solve the given system of differential equations. dx dt  =  3y + et…

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Q: If z = f(x,y) = tan x =t cose and y =t sin@. Use the Chain Rule method to find y as functions of t…

A: Given that z=f(x,y)=tan-1xy Where x=tcosθ,y=tsinθ Substituting, the values,…

Q: 10. Show that the function f(x, y, z) = 2z³ – 3 (x² + y²) z satisfies the Laplace equation.

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Q: Consider the functions z = -2e" In y, x = In (u cos v), and y = u sin v. dz dz (a) Express and du as…

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Q: Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2x

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Q: Ôz 12. If z = cos(x y)+ y cos x , where x=u +v and y=u-v use the chain rule to find and ди

A: Given: z=cosxy+ycosxx=u2+vy=u-v2 Recall the chain rule,  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u…

Q: Suppose z = x² sin y, x = -s² – 21² , y = 8st. dz A. Use the chain rule to find and * as functions…

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Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: 10. Show that the function f(x, y) = e=2y cos 2r satisfies the Laplace equation.

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Q: Show that the functions In x , In(x2) linearly dependent (0, co) are on

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Q: 6x Find the linearization L(x,y) of the function f(x,y) = e cos (y) at the points (0,0) and

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