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Functional Analysis

The linear isometry F:l'"\\to" (l^infinity)' given b F(y)=fy, y"\\isin" l' is not surjective

Functional Analysis

Rose wants to buy a car on hire purchase for N$75,000.00 at the rate of 11% p.a. repayable using monthly installments for a period of 3 years and 10 months. (No deposit was required). Use the given information to calculate the:

a. Total amount of money expected to be paid to the Hire Purchase Company over the years. (5)

b. Monthly installment to be paid by Rose (5)

Functional Analysis

Emmerson invests N$100,000.00 on a monthly basis, at the end of each month at an interest rate of

8.5% compounded quarterly.

a) How much will he have after 3.5 years?

(6)

b) How much interest does he earn on a monthly basis? (Hint: Calculate the monthly average).(4)

Functional Analysis

If a closed map F is bijective then its inverse F^{-1 } is a closed map.

Functional Analysis

If a closed map F is bijective then its inverse F ^{-1} is a closed map.

Functional Analysis

Given the demand function

Pd=35βQ2

and the supply function

Ps=3+Q2.

Calculate the producer surplus for the supply function.

Functional Analysis

Say True or False with proof

Q1. If π(π₯) = 2|π₯ β 1| and π(π₯) = 3π₯ β 10,

then πππ(1) = 12.

Q2. (β2, 1,1/2)β πΈ Γ π Γ πΉ.

Q3. The domain of the function f defined by π(π₯)

=β{(3-x)/(x-2)} is R-{2}.

Functional Analysis

`Represent the rational functioο»Ώn f(x)=1/3x-1 using its table values and graph`

Functional Analysis

x=R^n

x=(x1,x2,x3,x4,....,xn).

y=(y1,y2,y3,y4,....,yn)

d(x,y)=β((x1-y1)^2+(x2-y2)^2+(x3-y3)^2+......+(xn-yn)^2)

Show that d is metric on x

Functional Analysis

For an example of a discontinuous linear functional on a normed linear space