Let F be a vector-valued function such that 1 1+ t²⁹ F' (t) = = tet. 3t² and F(0) = (-1, 0, -2) 1. Determine F(t). 2. Find a vector equation of the line tangent to the graph of ♬ at t = 1.

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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IV. Let F be a vector-valued function such that
(te
1
1+ t²
F'(t) =
3t²
and F(0) = (-1, 0, -2).
1. Determine F(t).
2. Find a vector equation of the line tangent to the graph of ♬ at t = 1.
Transcribed Image Text:IV. Let F be a vector-valued function such that (te 1 1+ t² F'(t) = 3t² and F(0) = (-1, 0, -2). 1. Determine F(t). 2. Find a vector equation of the line tangent to the graph of ♬ at t = 1.
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