Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

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Q: ind [r(t) · u(t)] and Ir(t) x u(t)] in two different ways. dt r(t) = ti + 5t2j + t³k, u(t) = tk (a)…

A: Solving

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Q: 5. Differentiate with respect to x: SET A. 5e

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Q: the

A: We will find the derivative.

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Q: Find r'(t) r(t) = 6Vti + t²V¢j + In(2 )k r'(t) =

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Q: For nEN, simplify: 1 +1+2+ +4+ +8+ 금+ 1 .+2"-1+ 2n-1 (A 2" - 21-n+1 2" +2-n 2n - 2-n 3 D 22n - 23-2n

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Q: 5. Find the general solution: 9y" + 12y' + 4y = 0.

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Q: 5 x X LOS

A: Given: I=∫0πsin5x2cos7x2dx  ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

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Q: 2x (x- 3)2 .

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Q: What I Have Learned Let us now measure what you have learned in this module. Choose the letter of…

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Q: Two numbers have a sum of 72. What is their product if it is a maximum? (A) 1296 B) 1297 c) 1298…

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Q: (

A: We will find the centroid of the triangle.

Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

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Q: Write the expression as a single Integral -3 1. Sf f(x)dx + S, f(x)dx = -3 - 3. S f(x)dx + S, f(x)dx…

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Q: Change the order of integration. f(x, y) dy dx Jo

A: 0≤x≤10≤y≤xRegion bounded by:x=0, x=1y=0, y=x

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