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Thursday, November 20, 2008

variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parameter
make the coefficient of y" unity by dividing by x

find CF in the form Ay1 + By2 (using trial and error or some other method)
find the wronskian
and then find the PI as shown below





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Wednesday, November 19, 2008

time and work problem

X can do a piece of work in 2 hours, while Y can do the same piece of work in 4 hours.What is the time taken if X and Y do the work together?

converting to rate (quantity of work per unit time)

X can do (1/2) of the work in one hour
Y can do (1/4)th of the work in one hour

X+Y combined can do (1/2)+(1/4)=(3/4)th of the work in one hour

therefore X and Y combined will need 1 / (3/4)
or (4/3) hours to complete the work

that is 1 hour and 20 minutes

try the following page for some formulae time and work

other word problems with some explanation


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Tuesday, November 18, 2008

partial fractions

put 1/ [x(1 + x ² )] into partial fractions

other examples
put into partial fraction 1 / {(x^3) + 1 } -----> (partial fractions problem)

put 1/[ (x)(x-2)(2x-1)] into partial fractions ----------partial fraction


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Saturday, November 15, 2008

integral of ln(x) using integration by parts

find the integral of ln(x)

make it into ln(x )*1 {remember ILATE rule} and then start off integration by parts
some other examples
integral of (e^(ax))cosbx using integration by parts ----------> (integration by parts)

.∫ (x²) sin x dx using integration by parts ----------> (integration by parts)

integral of { sqrt{1+x^2} } / {x^2} using integration by parts ----------> (integration by parts)

∫ arc(tan4x) dx ----------> (integration by parts)

other examples on problems in math --------math problems

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Friday, November 14, 2008

integration by substitution

evaluate integral of e^(2x) / sqrt [1 + e^(2x)]

some other examples
integral of ( ( 4 - x^2 )^( 3/2) ) with limits 0 to 1--------------integration by substitution

integral of e^{x^(1/3)}-------------- e^{x^(1/3)}

integral of ( ( 4 - x^2 )^( 3/2) ) with limits 0 to 1--------------integration by substitution

more problems on integration -----------problems on integration

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Tuesday, November 11, 2008

obesity in children

I recently read an article on how the arteries and heart problems of some obese children as young as 10 year old was similar to that of 40 to 50 year old people.

Basically it seems to be the fault of parents, that a lot of small children end up getting fat. Some parents do not seem to know the importance of proper diet and good exercise.

I guess the children of today spend more time watching tv, and playing video games or on the computer, than playing outside. Also some parents (single working moms due to divorces etc) do not seem to have enough time to cook healthy meals for their children and instead just buy fast food /prepacked/processed /cooked food /junk food high in fat and carbohydrate content from chain stores which need not always be healthy.

Some of the government subsidies for corn farmers lead to some components like high fructose corn syrup (HFC) showing up in many places in place of ordinary cane sugar.

Children are easily misled by marketing gimmicks into consuming carbonated sweetened drinks which are fattening.

In the old days children would walk or ride cycles to school. But nowadays parents are afraid of traffic and drive their children to school or send them via auto's or buses.

Overweight children are more likely to have problem as overweight adults.
Some of the problems like heart problems, diabetes (type 2 ?), breathing difficulties, high blood pressure , depression etc may be due to obesity.

Wednesday, November 5, 2008

what do girls carry around in their handbags ?

The common items seem to be

hair brush
hair spray
perfume
nail file
cell / mobile phone
makeup items / kit
money
coins ,currency notes
credit cards
keys
tissues
pictures of spouse/kids
pens / pencils
tampon / pad
hand sanitizer
bills
receipts

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Tuesday, November 4, 2008

problem on L'Hospital's rule

evaluate limit of (1+2x)^cotx as x-->0

it is of the form 1^infinity which is indeterminate
hence take log and adjust into 0/0 form before starting
to apply L'Hospitals rule

for more details refer L'Hospital's rule and indeterminate forms







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There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work