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chapter3.page11

# chapter3.page11 - diﬀerentiable if each of its entries...

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2. VECTOR-VALUED FUNCTIONS 11 Example 2.2 . Suppose v ( t ) = t t 2 t 3 - 2 , x = 1 t 2 e t , and A ( t ) = 1 t 3 - 4 t + 5 1 0 2 sin( t ) 2 0 1 . (a) Find v ( t ) + x ( t ); (b) Let f ( t ) = e t , ﬁnd f ( t ) x ( t ); (c) Find A ( t ) x ( t ) Solution (a) v ( t ) + x ( t ) = t t 2 t 3 - 2 + 1 t 2 e t == t + 1 2 t 2 t 3 - 2 + e t ; (b) f ( t ) x ( t ) = e t 1 t 2 e t = e t t 2 e t e 2 t ; (c) A ( t ) x ( t ) == 1 t 3 - 4 t + 5 1 0 2 sin( t ) 2 0 1 1 t 2 e t = 1 + t 2 (t 3 - 4t + 5) + e t 2 t 2 + e t sin( t ) 2 + sin( t ) a 2.2. derivative and integrations of vector-valued functions. A vector-valued function is continuous if each of its entries are continuous. A vector-valued function is
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Unformatted text preview: diﬀerentiable if each of its entries are diﬀerentiable. • If v ( t ) is an vector-valued function, then the derivative d v ( t ) dt = v ( t ) of v ( t ) is a vector-valued function whose entries are the derivative of corresponding entries of v ( t ) . That is to ﬁnd derivative of a vector-valued function we just need to ﬁnd de-rivative of each of its component....
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