DJJerome1976

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These are questions asked by DJJerome1976

I am playing around with certain "simple" integrals, and came across this strange behavior in Maple. Maple is able to integrate sin(x)^(1/2)*cos(x)^3, but not sin(x)^(1/3)*cos(x)^3. Any idea why?

trig_integral.mw
 

int(sin(x)^(1/2)*cos(x)^3, x)

-(2/7)*sin(x)^(7/2)+(2/3)*sin(x)^(3/2)

(1)

int(sin(x)^(1/3)*cos(x)^3, x)

int(sin(x)^(1/3)*cos(x)^3, x)

(2)

 

Why does the iscont( ) function declare that the square root function is continous over Riscont_error.mw
 

iscont(sqrt(x), x = -infinity .. infinity)

true

(1)

``


 

Download iscont_error.mw

 

I am able to generate random polynomials with non-zero coefficents, and define sets of all the positive divisors of the leading coefficient and the constant terms. My question is this, how may I apply the rational zeros theorem to generate the set of all possible rational zeros of the polynomial. I basically need to form all the possible quotients (positive and negative) with numerator in one set and denominator in the other set, ignoring duplicates. The attached worksheet has what I've done so far.rational_zeros.mw
 

attempt := 1; while attempt > 0 do q := randpoly(x, coeffs = rand(-9 .. 9), degree = 3, dense); if nops(q) = 4 then attempt := -2 end if; attempt := attempt+1 end do; q

5*x^3+3*x^2-4*x-8

(1)

NumberTheory[Divisors](coeff(q, x, 3))

{1, 5}

(2)

NumberTheory[Divisors](coeff(q, x, 0))

{1, 2, 4, 8}

(3)

``


 

Download rational_zeros.mw

 

I am generating a lot of random graphs in Maple, and I need to generate the LaTeX code for these graphs. It has been working very well, until now, when I got to weighted graphs. The LaTeX code does not create the weights. I know I can modify the code to add the weights, but my question is two-fold: why aren't the weights automatically generated? is it possible to have the weight automatically generated, how? Nothing in the documentation appears to address these issues.

 

An example of what I attempting to do is in the attached worksheet.

Thanks!

graph.mw

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!

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