R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

Q: y(6) – 4y®) +6y® - 4y'+y =7

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Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

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Q: •Cx²+Jy'tuxy X y(2)21 use Rennoull EQ.

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Q: 35 Find the extrem poinbs of Pcxy)=xy Subject to X+y=20.

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Q: In(t – 8) 5 7t3 b. y= | 8t

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Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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Q: 1. (J · K) v (~ J. ~ K) / :. J = K

A: There are three expression in the given logical statement. They are J.K ~J.~K J≡K We prove the two…

Q: Q4) Choose correct answer: 1 csin-(cosx) dy dx = 1-п а. 1-n b. -2 1+n С. 2 1+n d. -2

A: The given expression is ∫01∫0sin-1cosxdydx.

Q: Given f(x, y) = ye" + 2ry³ + xy, find fzz, fzy, fyz, and fyw

A: Use partial differentiation to determine the values of given terms. Partial differentiation is…

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: For which values of r is the function y =t" a solution of t?y" – 5ty' + 8y = 0 Select one: O a. r=…

A: Given differential equation is euler-couchy homogeneous differential equation which can be solved by…

Q: Q1/ If z = f(x, y) and z* - y? = 6x²y°z7 Find: and dz

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Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

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Q: Q3. Find y= fx) such that y

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Q: y'47y'+12y = 2le", y(0)=,0)=-10 .

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Q: 8. Let a2 + xy³ + 2x = 11. Find y"(x) at the point (1, 2). %3D

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Q: If WX = 3t - 45 and VY = t, what is Y? W V Y こ

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Q: Given f(x, y) = sin(x2) + xy³, find Duf(x, y) where u is in the direction of (1, 2). What is Duf(-2,…

A: To find the directional derivative of given by function

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: Q Evaluede ds where c is Linesegment fromcい3)のしら、-2)

A: Given integral is ∫c2x-y2ds from (1,3) to (5,-2)

Q: 11 FCF)dt= fCx) dx =- 43 then 1.

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Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: キIND THE SOLUTIONS to THE DEFF ERENTIAL EQUATI ON y'= x? tyZ %3D メY

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Q: a) Find the value of + 1) tdt by using the substitution u = +1

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Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: The function f)= 2 Vx-3'+6 is not one-to-ane. O True O False

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Q: y' – 2y = 3e'

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Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

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Q: uppose that x + y = 2. What is y" at the point (1, 1)?

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