Proof In Exercises 61-68, prove the property. In each case, assume r, u, and v are differentiable vector-valued functions of t in space, w is a differentiable real-valued function of t, and c is a scalar.
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True or False? In Exercises 73-76, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
If r and u are differentiable vector-valued functions of t. then
Suppose that F : R3 â V 3(R) and G : R3 â V 3(R) are twice differentiable vector fields. Also, consider a differentiable scalar function f : R3 â R. Prove each of the following: A. â⢠FÃG = G⢠âÃF âF⢠âÃG . B. âÃ(fF) = f âÃF +âfÃF.
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Transformation of a vector Valued-Valued Functions In Exercises 41 and 42 use a computer algebra system to graph the vector-valued function r(t). For each u(t), make a conjecture about the transformation (if any) of the graph of r(t). Use a computer algebra system to verify your conjecture.
(a)
(b)
(c)
(d)
