alla's blog

transferring standard math

If you have a standard math, complicated expression in your Maple worksheet that you would like to include in a blog in this venue, what's the most economical way to copy & paste it?

Alla

scientific notation

When inserting standard math into a text region, Maple insists on converting even simple decimals like 0.01 into scientific notation.  Can I suppress that?

Allan

difference of two cubes

If x -1 is regarded as the difference of two cubes, can Maple factor it?

Alla

Dirichlet function

Can Maple graph the Dirichlet function?

f(x) =   {0,   if x is rational
            {1,   if x is irrational

Alla

 

limit of sqrt(0)

Maple says that the limit of sqrt(x), as x goes to 0, is 0, but Edwards of Larson et al. says that it isn't because "f(x) = sqrt(x) is not defined on an open interval containing 0 because the domain of f is x > = 0." 

 Comments?
 

Alla

cube roots of negative numbers

Why does the following give me an imaginary number?

 (-.008)^(1/3);

discontinuities

My calculus book says that y = (x^2 - 2)/(x - sqrt(2)) is discontinuous at 2, but Maple finds a limit of

 

unwith

Does the following error message mean that the only way to remove RealDomain is to exit Maple & then start a new session?

 unwith(RealDomain):

Limit problem

Here's a limit where Maple stalls:

Ø     limit((sqrt(h^2+4*h+5)-sqrt(5))/h,x=0,right);
Ø      

The best it can do is

Function limits at domain endpoints

My calculus text says that a function cannot have an ordinary limit at an endpoint of its domain, but it can have a one-sided limit.  So, in the case of f(x) = sqrt(4 - x^2), the text says (a) that it has a left-hand limit at x = 2 and a right-hand limit at x = -2, but it does not have a left-hand limit at x = -2 or a right-hand limit at x = 2 and (b) that it does not have ordinary two-sided limits at either -2 or 2.

So there are six possibilities.  Maple gives limit = 0 for all six.  Why the discrepancy?

Alla

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