DSE 2013 Paper Discussion

[Dreyfus]

Hey Neha...the method you used is for discrete compounding formula ie A=P(1+r)ⁿ { n is no of years and the formuale is for annual compounding)
And as per the ques the growth rate is instantaneous ie compounding is continuous, given by A=P*e^(r*t)

[neha:)]

How to do 21 and 25? (series 01)

[Granpa Simpson]

for Q21 use Descartes Rule of signs, the number of positive root is equal to the number of sign change in f(x) or less than that by an even number, and number of negative roots is equal to the number of sign changes in f(-x) or less than that by an even number..now in this case it is observable that there is no sign change in f(-x) so no negative root is possible. However for f(x) there is one sign change..so there is one real root.

[The Villain]

Q21..
Using descartes rule we observe that the fn can have 1 positive root or none.
Now diff it.It comes out to be strictly inc...so only 1 real root

[The Villain]

@,subhayu..we answered at nearly the same time :-p

[neha:)]

Thanks both of you :) Any idea about 25th?

[Granpa Simpson]

Cheers Ron...

[The Villain]

@neha..naah..havent done linear transformations yet

[kangkan]

x+1 and y+1 cant be expressed a linear function of the other..but one of arguments for f(x) can be xpressed as linear function of the other two

[neha:)]

Can you explain a bit more? I'm still not clear about it ..

[kangkan]

actually, i am also not 100% sure..let me just confirm it somehow

[The Villain]

for quest 39 and 40 series 1
I'm getting ans 39 a
40 d...pls confirm guys

[kangkan]

i think 40 is a...since they will wud like to change swap their bundles,they shud be willing to swap them one for one..hence px=py..and i am not sure if px=py=1 and px=py>0 are two diffrent conditions..we can always assume one price to be numerie right?

[The Villain]

Ya we assume one price as numeraire bt i guess they can swap bundles at any price bt it should be equal and positive..

[kangkan]

i am not sure about these two questions :(

[SoniaKapoor]

quest 1 and 2...pls help

[Granpa Simpson]

For Q1 use Lagranges Mean Value Theorem..in the question we are required to find out dx/dt which is the velocity..according to LMVT dx/dt of f'(t) will pass through f(b)-f(a)/b-a at least once in [a,b] if f is continuous and derivable in the region...thus dx/dt=(100-0)/(20-0)=5..thus answer will be d.

[Granpa Simpson]

For Q2 too use LMVT...take the interval [3,5] now since the function is differentiable then f'(x) can be represented as [f(5)-f(3)/(5-3)]=f(5)-f(3)/2.
or, 3<=f(5)-f(3)/2<=4.
or, 6<=f(5)-f(3)<=8.
or, 8<=f(5)<=10 [since f(3)=2].
so f(5) lies in the interval [8,10]

[SoniaKapoor]

Thanxx Subhayu..

[Granpa Simpson]

My pleasure...