Determine whether the following functions satisfy Laplace's equation dx? 0. dy? (a) z = -x²-y + 2xy %3D O The function satisfies Laplace's equation. O The function does not satisfy Laplace's equation. eTextbook and Media Hint (b) z = e*siny + e'cosx O The function satisfies Laplace's equation. O The function does not satisfy Laplace's equation.

Q: b) Differentiate (i) (i) the following functions clearly showing your working y = cos (4x4) y =…

A: Let us differentiate the functions with respect to x in the next steps.

Q: Find the differential and evaluate for the given x and d/x of the function, y = tan x, x = 0, dx =…

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Q: b) Find the potential P(x,y) attached to the exact ODE 2r sin(y) + x* cos (y) y = 0

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Q: Find the differential of the function. y = (2+cos?)1/2 dy=?

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Q: Find the position function of the particle moving along a line that satisfies the a(t)=4 sint-cos t,…

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Q: Differentiate the function g(p,9) in derivative and differential form. 5. Given two measurements p+…

A: Given that: Two measurements:   p±∆p and q±∆q

Q: dx sin y dt dy = COS x dt Find all r-nullclines and all y-nullclines

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Q: Find the differential of each function. (a) y = 1 + 5s dy = (b) y = e-u cos(u) dy =

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Q: Let x~B (mp) Find E (x') Metho d Moment ?

A: From the given information, X~Bn,p The probability mass function is, PX=x=nxpx(1-p)n-x,…

Q: roe-t sin(v3t) (i) * sin(V3t) dt]

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Q: Find the derivative of the function at Po in the direction of A. 1(x.y.z) = - 2 e* cos (yz),…

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Q: (c) Differentiate the following functions with respect to x. (i) х3 + 5y4 — 2 — 1. (ii) y = -…

A: Differentiate the given functions with respect to x.

Q: OFF The electric potential at a point (r, y) is given by V(z, y) = e-2* cos 3y. Determine the…

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Q: Find the differential of each function. (a) y = tan(V5 dy = 1 - v2 (b) у 3 1 + y2 dy =

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Q: Fu = x? + y? + z?, where x = e2t, y = e2t cos (3t), z du en at t= 0 is - dt

A: In this question, the concept of the derivative is applied. Derivative We can use a derivative to…

Q: 19. Differentiate the following functions. c) y = Vx ++ Vã sec (x³+1) cos ya d) y =

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Q: Differentiate with respect to t. y = a cos t + 2 sin t

A: The given equation is y=acost+t2sint.

Q: diff eq's: how to solve this ivp using another method than Laplace.  y"-a^2y=cos(a+t) ; a=constant.…

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Q: 6. Find the derivatives of the following: a) g(r) = sin(vi) dt %3D g(=) = /" Ve +4 dt

A: Please refer to the image below

Q: dy i. Find dx of y = x* Гcos @ Isin 0 ii. Let A=| cos e l, Verify A. AT = I

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Q: a) Compute when: x = 0 + cos0 y = 0 – sind 1 b) Compute when: x = 0 + cos0 y = 0 – sind c) Find the…

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Q: Use the differential dyto approximate Ay when x changes as indicated. y = V3x – 2; fromx=2 to x=…

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Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) =4T cOS nt…

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Q: 1. e+sin z- COs I 2e-u(t)dt

A: Part(1):-

Q: (d) +ỷ =0 dy dt (e) (f) d²y dt² d³y dt3 + sin(t + y) = sin t +t + (cos² t) y = t³ dy dt

A: To find out the order of the differential equation and also we need to write down that the…

Q: y"+2+y=e^5t y(0)=0 У (0)-5

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Q: Find the differential of each function. (a)     y = etan(?t) dy =        (b)     y =    1 +…

A: we have to derivate a given a function y=etan t  let t be a function then we have  dy=etantd(tan t)…

Q: Let the position at time t seconds of a particle moving in a coordinate line be given by s(t) =…

A: Formula used:

Q: y" + 2 + y = e5t ;y(0) = 0; y'(0) = 5 %3D

A: Recall: Ly'(t)= sY(s)-y(0) Ly''(t) = s2Y(s)-sy(0)-y'(0)  Leat = 1s-a

Q: Let y = tan(2a + 8). . Find the differential dy when a = 5 and da = 0.2 34.47 Preview Find the…

A: To find the following a). The differential (d y) when x = 5 and (d x) = 0.2. b). The differential (d…

Q: Evaluate: L{t f -t e2t Cos t dt}.

A: Evaluate: Lt∫0te2t costtdt First of all we find    L(cost)=ss2+1L(e2tcost) =…

Q: Differentiate the function.  z =A / y 10  + B cos y

A: Given function:                     z=Ay10+Bcos y Here we know that:                     A and B are…

Q: dy dy For the function dt 7 cos t, the third order derivative dt3 is %3D

A: derivative with respect to t first oder derivatinve dydt is ddt(y). (which is given in the…

Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

Q: Find the differential of each function. (a) y = 3 + 5s dy = (b) y = e¬U cos(u) dy =

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Q: esin 2x + sin(e2"). Find dy Show your work. dæ Let y =

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Q: Find the differential of each function. (a) y = tan V3t dy = (b) y = 1 + v2 dy =

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Q: Find the differential of each function. (a) y = tan(v7t) dy = 4 - v2 %3D y = 4 + v2 (b) dy = %3D

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Q: The acceleration of a particle moving back and forth on a line is a(t) = n? cos(at) m/sec? for all…

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Q: cos(x) If f(x) = ["(@) "g(x) V1 + t3 dt, where g(x) = S [1 + sin(t²)]dt, find f'(;). 1 %3D

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Q: Find the points on the interval -n s0s n at which the cardioid r = 1- cos(0) has a vertical or…

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Q: 3 For which values of a E R the tangent plane to the graph of f(x, y) = 1+ sin(ax + y²) at the point…

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Q: (dr Ifr=a cos ti +a sin tį+ at tan 0 k, find dt dr at t = 0. dr?

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Q: Find the differential of the function. Z = e-8x cos(5xt) dz z = dx + dt %3D

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Q: Let y = 4/T. Find the change in y, Ay when x = 1 and Ax = 0.3 Preview Find the differential dy when…

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Q: ds The velocity of a particle moving back and forth on a line is v = = 6 sin(2t) m/sec for dt all t.…

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Q: -y=- coS I: dz

A: it is a first order differential equation and it is linear differential equation

Q: Find the differential of each f (a) y = 1 + 4s dy =

A: (a) The given function is: y=s1+4s. The quotient rule of differentiation states that d…

Q: Determine whether the following functions satisfy Laplace's equation :0. ду? %3D dx (a) z = -x²+y? +…

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Q: 1.0 1.1 1.2 1.3 1.4 1.5 1.6 f (x) 7.989 8.403 8.781 9.129 9.451 9.750 10.031 d²y dy and dx Find at…

A: The solution is given below in the next step: