mixture

Saturday, January 31, 2009

problem on A.P. arithmetic progression

find the sum of all even natural numbers between 2 and 200 (both inclusive ) excluding the multiples of 3.

multiple of both 2 and 3 means multiple of 6 (lcm)

formulae on progressions A.P. G.P H.P. etc

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Wednesday, January 28, 2009

orthogonal trajectory of y(1+x ² ) = Cx

find the orthogonal trajectory of y(1+x ² ) = Cx
first form the differential equation of the given family
replace (dy/dx) with -1 / (dy/dx) to get the differential equation of the orthogonal trajectory
and solve the resulting equation

another example:orthogonal trajectory of y = (k/x)
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Tuesday, January 27, 2009

area bounded by |x| + |y| = 20

|x| + |y| = 20
corresponds to
x + y=20
x - y=20
-x + y=20
-x -y =20
the graph is shown below

required area = 4*area of right triangle

= 4 * (1/2) *20 * 20 =800 sq. units
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Monday, January 26, 2009

integral of (5x^3 + 8x^2 + 36x + 36) / (x^4 + 9x^2)

integral of (5x^3 + 8x^2 + 36x + 36) / (x^4 + 9x^2)
first do the partial fraction decomposition
refer partial fraction decomposition
then split the (x+4) /( x² +9) into two terms
the first one can be manipulated into u' / u form

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Saturday, January 24, 2009

limits for the correlation coefficient

find limits for the correlation coefficient

show that -1 <= r <=1 or |r| <=1

Monday, January 19, 2009

equation of tangent

find the equation for the tangent to y = x^4 at the point where x=2
first substitute x=2 into the given equation to find y to get the point (x1,y1)
at which the tangent is required.
find dy/dx and evaluate it at (x1,y1) to get the slope,m of the tangent
then use (y-y1) = m(x-x1) to get the equation of the tangent

Monday, January 12, 2009

software resources

portable apps are software that can be carried around on usb sticks, and will work without further installation onto the computer and can hence be run on any computer from which the user can access his portable data storage . Examples like portable versions of GNUcash ( accounting/financial management software) , firefox browser, bonkenc (for extracting music for cd's and changing them into formats like mp3), abiword portable version for wordprocessing , virtualdub portable version for video processing and capture etc
available at portableapps.com

some software for image resizing,adding text,watermark,crop, batch rename, screen capture are available at faststone.org some of the software are freeware and some are shareware
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