Functional Analysis Answers

A height of a shotput can be modelled by the function
H = -4.9t2 + 8t + 1.5
where H is the height in metres and t is the time in seconds.

1) At what point do you think the shotput was traveling the fastest? What factors did you use to make your inference?
2) Determine the average rate of change on a short interval near the point you chose in question 1.
3) Estimate the instantaneous rate of change at the point you chose in question 1
4) Were your answers to the average rate of change the same as the instantaneous rate of change, if not why not?

verify the equality: |u+v|2+|u−v|2=2|u|2+2|v|2, and. derive the theorem:the sum of the square so fthe diagonals of a parallelogram is equal to the sum of the square so the sides

What is the norm of the operator K from C[0, 1] into itself, if K is defined
by K (f )(s) = ∫ log |s − t|f (t) dt? (the integral taking from 0 to 1)

Let X be the set of all real-valued functions x on the interval [0,1],
and let x≦y mean that x(t) ≦y(t) for all t∈[0,1]. Show that this
defines a partial ordering. Is it a total ordering? Does X have maximal
elements?

range of function cos(sinx)

If Z is an (n — l)dimensional subspace of an n-dimensioned vector
space X, show that Z is the null space of a suitable linear functional f
on X, which is uniquely determined to within a scalar multiple.

If Z is an (n — l)-dimension£il subspace of an n-dimensioned vector
space X, show that Z is the null space of a suitable linear functional f
on X, which is uniquely determined to within a scalar multiple.