Integration, Maclaurin series, and radioactivity
1. integral (4x-x^2) ^ (1/2)from 0 to 4
i know that I should use completing the square
so i ended up with (-4-(x-2)^2)^(1/2)
however, it doesn't look right to me, May I get a helpful solution?
A certain radioactive isotope is observed to decay to 98% of its initial amount over ac) How long will it take the sample with initial mass of 100g to decay to a mass of 8g?
period of one year.
a) Assume that the sample has an initial mass of 100g. Find a function that represents
the mass of a sample as a function of time (in years).
b) What is the half-life of the isotope?
Find the Maclaurin series for the functions sinh(
x) and cosh(x) by using the Maclaurin
series for ex and the de nitions of sinh(x) and cosh(x) in terms of ex. Compute the radius
of convergence for each series.