If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g Cuv) + h lu-v).

Q: Evaluate fay'da + aªdy, where C is the rectangle with vertices (0,0), (1,0), (1,4), and (0,4)

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Q: dx 19) u = 4x + 9 4x +9 1 A) B) 2/4x + 9 + C + C + 9)3/2 1 + C V4x + 9 C) 2- S dx 20) u == 4x + 6 4x…

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Q: у" — 2у' + 5у 15x2 — Зх — 3 || - - -

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Q: 1) Linearize: 3x arourd 天=l %3D

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Q: dx Evaluate: 1) 2) -2x 3) 4) 5) 5-y'

A: *** As per our guidelines, we are supposed to solve only the first three problems/subdivisions.…

Q: FCx): 2x-5xナ3 find f'co).

A: We are solving the first question and for the next question post the question again and also mention…

Q: S-メー1)J r8-2) Cx+3) Cx+V)

A: Given,        ∫x2-x-1x-2x+3x+4dx

Q: By transforming to principal axes, reduce the quadratic form x' Ax for 2 2 1 A = 25 2 1 2 2 to a sum…

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Q: Solve for the orthogonal traysctories x*(3k-x) - ky². = x ? 2

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Q: Show that x +2 and oe) = *+6

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Q: sVx? + 1d: Idx = 1

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Q: ²*6²²y dy) dr 3

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Q: Demonstrate the following relationship involving the dot product and cross product (a) u. (v x W): =…

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Q: 2X +3 2x' +6x² +4x

A: This is too lengthy kindly repost the remaining parts.

Q: IF x= t +t¯ AND y=tª+t^ y 1. FIND d? a.) a ct +t^) 6.) 2 Ct-ta) ース C.) 2 Ct+ 1- 七ス d.) MOME OF THESE

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Q: Give one example that: 1. Show that 1/2 (x - x^T) is skew symmetric. 2. Give one example that:Show…

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Q: What are parts d-j?

A: As per the guidelines of Bartleby, solution of only first 4 parts are given.The remaining 3 parts…

Q: If y 3 , then dx 5x2-3 10r2 3V/5x2-34 35x2- 3) 5x2-3 10x 3 3(5x2-3)2 10r 3 35x2-3)

A: Find the derivative of the given function.

Q: х — у—1 3y – 3x – 3y (1) = 1 у (1) %3D 1

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Q: ZA'B'C' is the image of LABC following the reflec- tion of ZABC across line (. If mZA'B'C'= + 20 and…

A: Given: m∠A'B'C'=x5+20, m∠ABC=x2+5 We know that when we take reflection of a triangle across any line…

Q: 8- Evaluate a) ſe² + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) J 73-9x²+8 esc²) dx Csc2 - х3-9х2+8

A: We have to use proper substitutions.

Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

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Q: Let flox) - I=39 1-3x %3D

A: Answer and explanation is given below

Q: Find Lte " sin 41]. -2r

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Q: a'+3ab? If 3a’b+b³ 3x°y+y' _ x³+3xy² X_ y Prove that a b

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Q: 2-5 Secxtanx edx 4-Sečx

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Q: Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or…

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Q: Ex Fezy)= 3x+ 8x fom <2) F(Zx).2 8+ x9 =

A: Given: f2x=3x2+8x For finding value of f'2, we differentiate given function with respect to x

Q: %3D 2-FX) =CSC X 3-FX) cotX %3D 7- Fx) = Cos3Y

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Q: A Find a numbel z That satisfies The condubion g af The MUT I dx= 9 4 -4 O -a 0-15

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Q: Integrate: - da 9x2+16 O In (3x + v9x2 +16) + C O In (3x + V9x2 +16) +C ㅇ tan ' (뚜) + C 0 tan1 (부) +…

A: Given ∫dx9x2+16

Q: 7. Evaluate * (D5 – 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯x + Сze* +C₁е²x cos3x +C5e²x…

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Q: f) = Vx?+4x+4 9=3 Find (f") (@)

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Q: Cannot solve

A: Multiplying and dividing first term by secx and second term by tanx of left hand side of equation ,…

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: VXEN, 3yEZ s.t. x + y^2 = x - y O TRUE O FALSE

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Q: If m^3 divides v^2, then m divides v

A: Let, m3 divides v2        now, m2 divides m3 and m3 divides v2        =&gt; m2 divides v2…