Hi,

I just noticed something rather peculiar (well, to me, at least). When I compute the limit

limit((1-1/x)^(-x),x=-infinity)

as is, I get the expected result of exp(1).

However, if I load the RealDomain package prior to computing the limit,

with(RealDomain):

limit((1-1/x)^(-x),x=-infinity)

I get that the limit is undefined. 

Any ideas as to why that is the case? Thanks!

Hi,

I would like to animate the solution to

x'(t)=y(t)

y'(t)= -4x(t)

that passes through x(0)=2, y(0)=1 as it orbits (0,0). I need to include the phaseportrait as the background. Any ideas on how to accomplish this?

Thanks!

Hi,

My question is fairly straight-forward, I hope someone has an equally straight-forward solution. I would like to be able to illustrate the convergence of the distribution on the mean of i.i.d random variables to the normal distribution. For example, I'd like to visualize (by way of a histogram plot) that as n increases arbitrarily, the mean of n i.i.d. exponential random variables with mean 10 converges to a normal distribution.

Thanks!

Hi,

I have a pretty simple problem. Given the following set of responses to a "yes (y)/no (n)" question, create a pie chart and a bar chart.

y, y, n, n, n, y, y, n, n, n, y, y 

I would like solution that does not involve coding the data, say y = 1 and n = 0. I am aware of the BarChart and ColumnChart commands in the Statistics package, but I can't seem to get them to work with nonnumeric data. Is there an easy way to do this?

Hi,

I've figured out several ways to accomplish this, using a series of commands, but is it possible using only dsolve to solve a first-order ivp involving two constants: the constant of integration and a constant of proportionality. For example, the type that arise using Newton's basic law of heating/cooling:

y'(t) = k*(y(t)-10), y(0)=70, y(1/2)=50

I welcome all ideas, especially if there is something easy I'm missing, thanks!