DJJerome1976

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These are questions asked by DJJerome1976

Hi,

I use the plots:-shadebetween( ) command quite a bit to visualize volume under a surface over a planar rectangular region. Is there a way, using this same command, to see said volume over a non-rectangular region? For example, the region bounded above by z = x^2 + y^2, having a triangle base 0<=x<=1, 0<=y<=x. If this command does not allow for this, is there some other solution?

Thanks!

How do I get Maple to reduce/simplify the following difference quotient to its lowest terms? Basically I need Maple to rationalize the numerator. Any suggestions on how to do this?

f := proc (x) options operator, arrow; sqrt(2*x+1) end proc

proc (x) options operator, arrow; sqrt(2*x+1) end proc

(1)

expand((f(x+h)-f(x))/h)

(2*x+2*h+1)^(1/2)/h-(2*x+1)^(1/2)/h

(2)

simplify((f(x+h)-f(x))/h)

((2*x+2*h+1)^(1/2)-(2*x+1)^(1/2))/h

(3)

rationalize((f(x+h)-f(x))/h)

((2*x+2*h+1)^(1/2)-(2*x+1)^(1/2))/h

(4)

``


 

Download rationalize.mw

I'm trying to approximate the solution of an IVP using Euler's method in the InitialValueProblem command and I keep getting this error (see attached worksheet). Can someone explain why? Thanks!
 

restart

with(Student[NumericalAnalysis]):

InitialValueProblem((D(y))(t) = t*y(t)+1/y(t), y(0) = 3, t = 2, method = euler, numsteps = 5, output = solution)

Error, (in dsolve/numeric) array output cannot be obtained for problems containing global variables

 

``


 

Download ivp_error.mw

Can anyone offer an explanation why the following error occurs, and how it can be avoided? Thanks!

 

plots:-shadebetween(2, 1/sqrt(-x^2+1), x = 0 .. (1/2)*sqrt(3))

Error, (in t) invalid input: nops expects 1 argument, but received 0

 

``

 

Download error.mw

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