Functional Analysis Answers

Show that the space L²(R) of all square of summable real sequence is a linear space over a vector field R

Show that the space L(R) of all bounded real sequence is a linear space over a vector field R

Show that the space B[a,b] of all bounded real value functions on the interval [a,b] is a linear space over a vector field R

Show that the space R[a,b] of all Riemann integrable functions on the interval [a,b] is a linear space over a vector field R

How fast is the size of the population changing after 1 minute? 

1. . Under a set of controlled laboratory conditions, the size of the population P of a certain bacteria culture at time t (in seconds) is given by the function P(t)= 3t²+ 3e^t+10, (t greater than/ equal to 0)

(i) What is the size of the population after 1 minute?

(ii) Find the average rate of change of P at t = 2 and t = 6?

(iii) How fast is the size of the population changing after 1 minute?

[Verify your answer by MATHEMATICA and attach the printout of the commands and output]

Describe verbally how to solve y=mx+c. What assumptions have you made about the value

of ?

If a third-degree polynomial has a lone x-intercept at x=a , discuss what this implies about the linear and quadratic factors of that polynomial

Kindly answer this as soon as possible. Urgent Elaborate each step.

Show that Euclidean space and unitary space are not compact. Explain each step.