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Q: 5 If u =x² +y² and v = 4xy, determine дх дх ду ду du' dv' du' dv

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Q: 5. If u = e1#1+az#2++anIn, where a² + a³ + · ·..+ a = 1, show %3D + = U dx?

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Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: 4 À =A, i + Ayj + Az kk and + Byj + Bzk prone ズx8 %3D Ax Ay Az B By Bz

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Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

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Q: In GL(2, Z,3), det 4. O 35 11

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Q: S cscycoty 1+cacy dy Select one: OA. - In (1+ csc y) + C OB. In (1+ csc y) + C OC. In² (1+ csc y) +…

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Q: 6.13 Show that t: = B,/[s//E=, (x;- %3D VI- r in (6.20). |

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Q: 2 dy y+ 2xy di feransigel deiklenin 2.

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A: First Order differential equation :        Consider the differential equation…

Q: 1- Two vecters n'and mª anl Said to be orthogenal if n'entzo T b. F a.

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Q: 20. 7 (xx + y), x= st, y=st s= 1, t = 1 %3D %3D

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Q: Evaluate o S, (4 – x²y?) dy dx

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Q: 1: find af/ox and af/ày.. ) (x, y) = Vx² + y²

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Q: o Evaluate , S, Só (x – 2y + 2z)dz dydx.

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Q: 1- (In x)² If u = In x, then dx=? e A) B В =-u)du .2 © [a | (1- u)du .2 (D (1 – u²)du

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Q: -5= =DS"S"?{(m-3)x²+³"(m - m x- ? y)'-4myx] dydx

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Q: . If u . v = 0 and u * v = 0, what, if anything, can you conclude about u and v?

A: Dot Product The Dot Product is written using a central dot: a · b This means the Dot Product of a…

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Q: . d the しいwits UI- Vタ+1 ユ ーリー! Cスリ る) しm 5) (Z,y)>(,) Cos Tzyl-a C)にm 反- vy Ca,y)Co)

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Q: 15. YABCIa stnight Ine, ZCRO, and D Mbecta C+ ZCBG, then Zx y

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Q: •1 Evaluate ſ, S, Saya xyzdzdydx S So Sirzava xyzdzdydx 2 0. Vx²+y²

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Q: 4. Find the temperature in a perfectly insulted bar with c=1, u,(0,t) =u,(T,t)=0 and u(x,0) = 3x

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Q: - [o• P + 4)[5(t) + 48(t – 2)]dt. a) I b) I = P[8(t) + 8(t + 2.5) + 8(t – 5)]dt.

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Q: In 2 (In 2)2-y2 evx2+y² dxdy 0.

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Q: 1- In x)² If u=In x, then dx=? L'a-wdu A B

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Q: 19. Evaluate ra emax (b²x², a°y') dy dx, Jo where a and b are positive numbers and max (b²x², a²y²)…

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Q: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

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