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Math can be difficult to understand, but it's important to learn how to Find r(t) if r'(t).

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r(t)= f(t) i + g(t) j + h(t) k. r(0)= f(0) i + g(0) j + h(0) k. To make r(0)= i+j+ k, you need to make f(0)=g(0)=h(0)=1 . You found functions f(0) , g(0) , and h(0) that have the right derivatives, and

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Add your answer and earn points. nobillionaireNobley R (t) = integral of r' (t) = integral of ti + e^tj + te^tk = 1/2t^2i + e^tj + (te^t - e^t)k + c r (0) = j - k + c = i + j + k c = i + 2k

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To find A, B, and C, use r (0) = (that is, let t = 0): = . ==> A = 1, B = 0, and C = 3/2, by equating like entries. Hence, r (t) = t^4 + 1

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AGRFTr. Answered 2021-10-18 Author has 95 answers. r ′ ( t) = t i + e t j + t e t k. r ( 0) = i + j + k. Integrate each component of r ′ ( t) separetly. For the first component: ∫ t d t = 1 2 t 2 + c 1. The

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