Differentiation and Integration of Vector Functions Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the vector derivative for

(2) Find the vector derivatives and for

(2) Find the vector derivatives and for

(4) Find the indefinite vector integral

(5) Find the indefinite vector integral

(6) Find the indefinite vector integral

(7) Given determine so that

(8) Given determine so that

(9) Determine so that the parametric equations for the tangent line to the graph of the vector function at the point corresponding to are

   and    .

(10) Find the first and second derivatives of the following functions:   





.

(11) Determine so that given

.

(12) Determine so that given

(13) Find all such that and are parallel for all given

(14) Prove that if is a differentiable vector function such that then

(15) Prove that if and are differentiable vector functions, then

(16) Prove that if and are differentiable vector functions, then

(17) Determine values for and so that the following vector functions  







are smooth over

(18) Find a value of and such that



and

(19) The velocity of a particle moving in space is Find the vector so that the particle's position as a function of is

(20) The acceleration of a moving particle is Find the vectors and so that the particle's position as a function of is

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