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Wednesday, October 29, 2008

evaluate .∫ [1 / {x lnx}]dx

evaluate ∫ [1 / {x lnx}]dx

put u = lnx find du, substitute into the given integral and then
evaluate





another example
evaluate integral of { e^(1 /x^2)} / {x^3} substitution

integration formulae



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Tuesday, October 28, 2008

derivation of mean and variance of binomial distribution

derive the mean and variance of the binomial distribution
now to find the variance, we rewrite x^2 as x(x-1) +x before we start out



for explanation of mean of poisson distribution try the link mean of poisson distribution

for explanation of mean and variance of discrete uniform distribution try the link mean of the discrete uniform distribution



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Monday, October 20, 2008

solving a second order differential equation

solve y"-y'+y = 1

rewrite the equation as (D²-D+1)y = 1
replace D with m to get the auxilary equation
write the C.F. and then proceed to the particular integral (PI)

Friday, October 17, 2008

german 480 billion euro bailout

While a lot of noise was being made about the american bailout, the German parliament has hastily approved a 480 billion euro (approx. $650 billion) rescue plan for the financial sector, even though there is not as much of a mess as in the USA., (but the economy sure seems to be slowing down to a crawl)
Most of the money is for lending guarantees for banks and some of the money may be spent on buying up risky assets.
A major difference seems to be that banks participating in the plan will have to obey government conditions on executive pay, directions on lending, more government oversight etc.

At the same time the german government does not seem inclined to help bailout the beleagured carmakers in the auto sector.


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Thursday, October 16, 2008

Iceland

Iceland had won "the best country to live in" last year, when the stock markets were booming and icelandic companies were bent on acquisition ventures around the world . But this year Iceland seems to be the first country to be in a complete mess due to credit crunch.
It started off with problems in some of the bigger banks in Iceland. You have to remember that bank assets in Iceland were unnaturally large (around nine times the annual GDP) . The banks had been operating in many other countries besides Iceland following the deregulation in the 1990's . Some of the city councils in England had lots of money invested in the Icelandic banks!! These banks were also financing a lot of deals in Britain. With liquidity drying up in the global markets , the huge icelandic banks were unable to refinance the big loans they had given out.
England went to the extent of threatening seizing some of the assets of icelandic the banks in england
The government /central bank of iceland stepped in and took control of some of the huge banks.

This led to the stock market declining by around 77% { The benchmark ICEX from around 2300 to 700 } and the icelandic currency "krona" has lost most of its value.
Icelandic officials are looking for loans from Russia to tide over the crisis and might have to make some sort of adjustments using its oil gas exploration/rights.
Iceland imports a lot of food articles and the fall of the krona is having inflationary effects.Suppliers to icelandic importers may have started to cut down on credit because the importers may find it hard to find forex. with lack of clarity on the exchange rate.

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Wednesday, October 15, 2008

Will the banks lend out any of the $125 billion of the government investment

The US government is persuading nine banks to accept $125 billion of government investment.But there is no guarantee of any of the money being used in such a way to ease the liquidity crunch as the government does not seem keen on getting any control of the management side of the bank to dictate how the money is to be spent, as the treasury is not seeking voting stocks for the money it is investing

There seems to be a good chance of at least some banks just hoarding the cash to shore up their balance sheets and the fed may not be able to do anything about it.

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Tuesday, October 14, 2008

slowing of global economic growth

The whole scene of global economic growth might be slowing down considerably due to the credit crunch leading to loss of jobs, and loss of demand for manufactured items. This might lead to severe slowdown of some of the drivers of growth in the last few years like the chinese economy are highly dependent on export to the USA.

Most americans have been living far beyond their means and may be deep in debt, and the slowing down may lead to lower earnings, smaller paycheques, slump in home equity and tightening of spending if they are wise.

The figures at the retailers seem to indicate a slowdown in consumption


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if an obviously obese person asks you if he/she is fat

I guess your answer will depend on how much you care about the person.

some possible options may be

try to change the subject.

you are just big boned.

you are just on the large side.

you look good just the way you are.

try to comfort the asker and suggest healthy food and regular workouts





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Pepsico might cut some jobs

Pepsico the manufacturers of Pepsi-Cola drinks, Frito-Lay snacks and Quaker foods seems to have been hit by lesser demand due to the economic slowdown.

People seem to have cut down on the intake of bottled water, carbonated drinks etc. due to the higher gas prices and the general gloom in the economic scenario. It is likely to cut around 3300 jobs (nearly 1.8% of its workers). It might also close upto six plants and most of the job cuts are likely in the fourth quarter

stick shift (manual ) or automatic, which is your preference?

I think automatic transmission is for the lazy. It might be more expensive when repairs happen. It might lead to accidents since it opens up opportunities for other distractions like texting etc.
Stick shift gives you more control over the vehicle and helps you get more power from the engine when needed. The extra control might give better mileage if manual shift is properly used. The clutch change etc. are usually less expensive. I personally drive a manual shift and I like it.




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state elections in india are announced

The Indian states of Rajasthan, Delhi, Mizoram, Madhya Pradesh and Chhattisgarh will go to the polls next month between november 14th and december 4th . But the election commission failed to mention the case of Jammu and Kashmir.

Parliamentary elections are also due in India next year and the state assembly elections might be a nice way to judge the attitude of the people.


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Friday, October 10, 2008

US govt. might buy stake in several banks

It seems that the U.S. government/treasury is getting ready to buy an ownership stake in a broad array of American banks. This seems to be for the first time since the last great depression .
According to the treasury secretary, this "program would be designed to encourage the raising of new private capital to complement public capital". But it seems that they only wants to buy nonvoting shares . It seems that a broad intervention might represent a vote of no-confidence in the entire banking industry and not just some troubled institutions. Hopefully at least some strings regarding compensation of top executives could be attached to the buy , but I very much doubt if that will happen.
Earlier, Britain had also started a sort of partial nationalization of its troubled banks by allowing them cash in exchange for stakes in the banks.






Wednesday, October 1, 2008

example of differentiation using quotient rule

find (dy/dx) if y = (x+5)/(x-3)

using quotient rule since y is of u/v form









formulae on differentiation




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integration using "by parts " rule

evaluate ∫ { lnx / [x^4]} dx

take lnx as the first function

{ lnx / [x^4]} dx = {lnx} { 1 / [x^4]} dx

= {lnx} {-1 /[ 3 x ³] } - {1/x}{-1 /[ 3 x ³] } dx

= {-lnx /[ 3 x ³] } - {-1 /[3 [x^4]] } dx

= {-lnx /[ 3 x ³] } + {-1 /[9 x³] } + C

= {-1/[ 3 x ³] } { lnx + (1/3) } +C



formulae for integration

another example on integration by parts


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