Q: biven that y=sin(3lncx)) is a solulion of x y" + xy' +9y=0, solue x y"+ xy' +qy=0 ; y()= 2 =y'().
A: Solve Cauchy Euler differential equation
Q: Let y=5√xFind the change in y, Δy when x=1 and Δx=0.4Find the differential dy when x=1 and dx=0.4
A: Given: y = 5xTo find: 1. ∆y at x= 1 & ∆x =0.42. dy at x = 1 & dx=…
Q: 4. Given F(x, y, z) = (xy²z²)i + (x²yz²)j + (x²y²z)k Find: a. Curl b. Divergence
A: Use the formula of both Curl and Divergence to determine their values. In partial differentiation,…
Q: (x – cos y)dx – sin ydy = 0 Of (x, y) = -xe-# +e-* cos y + k (y) ;f (r, y) = -e- sin y dy +k (y) Of…
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Q: а. y' +y tanx %3D sесх + сosx b. 1 -/dx+x?dy)=0 (x² - y?) C. yy' – 2y? = e* С. d. 1 -(хdy - ydx)3D0…
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Q: y In x – x In y = 4, y' y In (x² + y² )= 2 arctan 2) = 2 arctan y'
A: This question can be solved using the concept of differentiation of implicit function.
Q: Let y(t) be the solution of dy/dt = 0.3y(2 − y) with y(0) = 1. Determine limt→∞ y(t) without solving…
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Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II
A: w=cos8x sin2y , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3 ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…
Q: lim r.y)→(0,0) (4 + (x² + y²) In(x² + y?)) Dose not exist -00 00 1 4-
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Q: Q) Use the chain rule to express dy / dx in terms of x and y for the :following y =1-! 1 t = 1-x and…
A: Consider: y=1-1t and t=11-x. Calculate dydxin terms of x,y at x=2. Calculate dydt and dtdx using…
Q: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…
A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev
Q: Let y(t) be the solution of dy/dt= 0.3y(2 − y) with y(0) = 1. Determine lim t→∞y(t) without solving…
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Q: (a) i. Find Re{sec (x + iy)}.
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = tanh (x + 2y + 3z)
A: We have given fx,y,z=tanhx+2y+3z and we have to calculate fx,fy and fz
Q: dz (a) Use an appropriate form of the chain rule to find dx dz in terms of y in terms of x and if z…
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Q: HW 0 1f y=tanx show thats y" = -2Siny Cosy %3D
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Q: dy -y2+1,ysCJse Cantial cokditian.
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Q: dz Use chain rule to find at (u, v) = (1, 1) if dv z = z sin(y² – z + 1)4), e = 3u – v², y = vº.
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Q: dw Use an appropriate form of the chain rule to find dt 1 y = t, z = to w = 3 cos xy – sin xz3; t'…
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Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate dy and ∆y if x= and π /4 and dx =-0.1.
A: Given function is (a) Differentiating with respect to x, we get
Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is
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Q: dw Use the Chain Rule to find dt w = x²e²y cos(32), x = cos t, y = In (t + 2), z = t
A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x).
Q: aーメ ターメ2.y to い-X to cylindHcal coordin ates
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Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)
A: Given:
Q: 3. Let z = x?y + 3xy+ where x = sin 2f and y cos t. Use the chain rule to dz find when t = 0. dt
A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…
Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1
A: Topic:- function
Q: x + y3 -1 Еxample If u = tan prove that x- y ôu ди (i) x. + y. sin 2u
A: # we are entitled to solve one question at a time , please resubmit the other if you wish to get it…
Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…
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Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…
A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…
Q: (a) Find the solution of the limit using polar coordinate system. x² + y² x2 + y2 lim (x,y)→(0,0)
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Ã(x, y.z)=(4xy²-x')i+(2e"-ycos2xj+(x'siny k . and Əyəx Əx' əy² 'Əxôy Find:
A: Given - A→(x,y,z) = (4xy2-x5)i^ + (2exy-ycos2x)j^ + (x3siny)k^We have to find the following -…
Q: rsin z cos t dt lim 2.r
A: Use L'Hospital rule and fundamental theorem of derivatives to solve it.
Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D
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Q: Show that y +4 dy = 4 In lyl – 3 In |y + 1| + C y2 + y
A: To Prove: ∫y+4y2+ydy=4 lny-3 lny+1+C
Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =
A: First order Partial differentials
Q: ry lim (z.v)¬(0,0) + y² exists.
A: Please refer the attached image for complete solution.
Q: dz at (u, v) = (1,1) if du Use chain rule to find -z + 1);), = x = 3u – v², y = u® z = x sin( (y? |…
A: If the input of the function is more than one, then it is called a multivariable function. In this…
Q: y 1) x(In x – In y)dy – ydx = 0 Ans: = c (Xie, 2010) %3D 1+In y-In x
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Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21
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Q: dz Use the Chain Rule to find : z = = cos(x + 4y),x = 5t*, y = - %3D dt
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Q: dz Use chain rule to find at (s, t) = (0, 1) if ds z = 6x + y² tan e – st, y = s² – ť. x = ebs
A: Consider a function of multivariable where and . Then according to the chain rule for…
Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).
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Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·
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Q: xy*-dy = (a* lIn a – y (а* In a - y %3D
A: we have to find the differential of ax=y
Q: E). f(x, y) = sen?(r2 – 0²) + In(r0 + 0), r = Vx2 + y² 0 = arctan con -
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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…
A: Given integral is, It can be represented using Green's Theorem as,
Q: Q2) Use the chain Rule to find dw\dt of y w = =+2,x = cos²(t), y = sin² (t), z =, at t = 3
A: In this question,w is function of x,y,z and x,y,z are the function of t so first we find out…
Q: %3D %3D In MIMI2 9.5. Ly=, Wq= F and L== au Find : Po =? and P,= ?
A: A/B/c Queueing System: A is the interarrival-time distribution. B is the service-time distribution.…
Q: V4-x² E Evaluate the double integral (x² + y² )°dydx.
A: Convert Cartesian coordinate system into polar coordinates system.
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- Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.Prove that arctan x + arctan y = arctan(x + y) / (1 − xy), xy ≠ 1. Use the formula derived to show that arctan (1/2) + arctan (1/3) = /4Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy − βˆSxy