Video: Evaluating a Vector-Valued Function

For the given function 𝐫(𝑑) = 2𝑑𝐒 + (2𝑑² + 3)𝐣, evaluate 𝐫(0).

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Video Transcript

For the given function 𝐫 of 𝑑 equals two 𝑑𝐒 plus two 𝑑 squared plus three 𝐣, evaluate 𝐫 of zero.

The function we’ve been given is a vector-valued function. It’s a function whose range is a vector or a set of vectors and whose domain is a subset of the real numbers. We’re looking to evaluate 𝐫 of zero. In other words, we’re going to let 𝑑 be equal to zero in our function 𝐫 of 𝑑. To find 𝐫 of zero, all we do is we replace 𝑑 with zero in our vector-valued function. So 𝐫 of zero is two times zero 𝐒 plus two times zero square plus three 𝐣. Two times zero is zero, and two time zero squared plus three is three. So we find that 𝐫 of zero is zero 𝐒 plus three 𝐣, which is simply three 𝐣.

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