mixture: index of problems

groups
If G is an abelian group ,
let f : G -->G be defined by f(x) = xֿ¹ show that f is an automorphism on G problem on automorphism on abelian group

If G is a group and f :G -->G is defined as f(x) = a ֿ¹ x a for x in G and a is a fixed element of G
then show that f is an isomorphism of G onto G problem on automorphism in a group

analytical geometry

centre and radius of a circle

correlation and regression

derivation of regression line of y on x

limits for the correlation coefficient

changing recurring decimal to fraction

derivation of mean and variance of binomial distribution

derivation of mode of the binomial distribution

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approximation of an integral using binomial series

mclaurin's power series for ln(1+x)

word problem A man has 10 paise and 25 paise coins in his purse. The man has a total of 60 coins which amount to Rs. 8.25.
How many 10 paise and 25 paise coins does the man have in his purse? solution

The ratio of the incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 . If each of them saves Rs.200/- per month, find their monthly incomes. solution

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? solution

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index of math problems

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Tuesday, December 16, 2008

index of problems

Integration formulae

integral of 1 / [9 + 7 cos² x]

integral of x^3 / sqrt(9 - x^2) using substitution

integral of tan ² x secx using substitution

integral of ln(x) using integration by parts

evaluate ∫ [1 / {x lnx}]dx

integral of [sin(lnx) ]/ x ² using substitution

problem on integration using trigonometry formulae integral of sin(5x)sin(8x)

integral of arc(cosx) using integration by parts

laplace transform of sin(t) from definition using integration

solving a quadratic equation by graphing

trigonometric identities

problem on changing the base of a log

integral using cauchy's integral formula

real and imaginary parts of ln(x+iy)

show that e^(ix) = cosx +i sinx using power series

problem on sequences If Sn is the sum of the cubes of the first n natural numbers, find the sum of 1 / sqrt(Sn) where n varies from 1 to 2000