Calculate[ri(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then by applying the formulas dr₂ dr₁ d[ri(t) · r2(t)] = r1(t) · + r₂(t) and dt dt d dr₂ dr₁ [r₁(t) × r₂(t)] = r₁(t) × + × r₂(t). dt dt dt r₁(t) cos(t)i + sin(t)j + 4tk, r₂(t) = 3i + tk =

Q: s(t) = (3t1/2+2)(5t1/3+1). Find the derivative of the function using the product rule and simplify…

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Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function f(r) = VI+ tª dt.

A: We will use the first fundamental theorem of calculus to evaluate the derivative.   The detailed…

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b). Find the preimage of the function.…

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Q: Optimize z=f(x,y)=20×x×y-(x2+y2), subject to x+y=4 Do in 45 minutes to upvote

A: Optimization problem

Q: Example. 4.8 A tank contains 300 litres of fluid in which 20 grams of salt is dissolved. Brine…

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Q: r(t) = 2t²1 - 4tj + 2t³k (a) r(t) (b) r"(t) (c) r(t)r"(t) (d) r(t) x r"(t)

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Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: The productivity of a country is given by f(x,y) = 13.34x yr, where x is the amount of labor and y…

A: The productivity of a country is given by fx,y=13.34x0.422y0.578, where x is the amount of labor and…

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Q: Calculate ri(t) r2(t)] and ri(t) x r2(t)] first by differentiating dt the product directly and then…

A: Given that ddtr1(t)×r2(t)=r1(t)×dr2dt+dr1dt×r2(t) Where                r1(t)=cos(t)i+sin(t)j+2tk,…

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A: Given: What does dr stand for in terms of r(t)?

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²i - 5tj + 3t³k 2 (a) r(t) (b) r"(t)…

A: Note: As per the guidelines, I have solved three sub-parts. If you want the solution to the last…