Functional Analysis Answers

A ball is thrown vertically upward with an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after t seconds is s= 128t – 16t2 what intervals of time is the ball less than 240 above the ground (after it is tossed until it returns to the ground)?

1. {x 0 sec < x < 3.5 sec and 4.5 sec > x > 8 sec}

2. {x 0 sec < x < 3 sec and 5 sec > x > 8 sec}

3. {x 0 sec < x < 2.5 sec and 5.5 sec > x > 8 sec}

4. {x 3 sec < x < 5 sec}

The growth of a $40 000 investment is shown in the table.

Time (years) Value ($)
0 40 000
1 42 600
2 45 369
3 48 318
4 51 459
5 54 803

Use the exponential regression function on your calculator to get the function. Round a to the nearest dollar and b to the nearest thousandth.

A normed space which is isometric to a Banach space is itself a banach space

X is a Normed linear space. T is a function from X to X. Then T is a bounded linear transformation

The starting equation for a question is f(x) = x^2 (base parabola function) and i need to change it to g(x) = f[1/4(x + 5)]. Would the point notation be like this: (x, y) --> (4x - 5, y) because the 1/4 inside the brackets is changed to a 4 when doing the point notation?

determine the x intercepts of the function:

f(x) = x^2 -8x -18

f(x) = x^2 -8x -18

1)Give one example of a normal operator on a hilbert space which is not unitary.Justify.
2)Give one example of a normed space which is not an inner product.Justify.

Prove every inner product vector space is norm space?

Find:
A = The (real) domain of the function f(x) = Ln| x |

B = The (real) domain of the function f(x) = 1/x