monochromators

monochromator is an optical device used to select a particular wavelength of light to pass through it.
for more details visit:
http://en.wikipedia.org/wiki/Monochromator

invention of plastic

plastic was first invented by alexander parkes in 1855.but in 1866 he started a company to produce it hugely , so in some of the sites it is given like invention made in 1866..

52/? is equal to 13/21?

say 52/x = 13/21
now x = (52 * 21)/13
x = 84

Integral of u/sqrt(u) du?

u / sqrt(u) is nothing but sqrt(u)..
now integrate
(1/2) * u ^(1/2 - 1)
(1/2) * u ^ (-1/2)

value of the expression

substituting the values in this expression
2 b - c/a

2( 3) - (8 / 2)
6 - (8/2)

6 - (4)

2

answer is :2

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What is the derivative of f(x)=((x^3)-3)/(5-(x^2))?

please show notation because i need it for test corrections Thanks!
sorry the denominator is 5-3x^2 not x^2

U/V rule
U - numerator
v - denominator

formula :
(V(dU) - U(dV))/(V^2)