## Trigonometric Integral...

```with(student);
[D, Diff, Doubleint, Int, Limit, Lineint, Product, Sum, Tripleint, changevar,

completesquare, distance, equate, integrand, intercept, intparts, leftbox,

leftsum, makeproc, middlebox, middlesum, midpoint, powsubs, rightbox,

rightsum, showtangent, simpson, slope, summand, trapezoid]
J:=changevar(cos(x)=y,Int(1/(1+a*cos(x)),x=0..Pi/2),y);

/1
|              1
|   ----------------------- dy
|                     (1/2)
```

## Maplet element BoxLayout...

To Maplet Experts: I am about to complete my maplet application developed in my desktop with screen resolution of 1440 by 900 pixels. My window layout has the following dimensions: width=850 and height=675. I am pleased with the layout of my application when shown in my desktop. I move my code to my laptop with screen resolutions of 1200 by 800 pixels. The layout of my application in my laptop is distorted and ugly even though I adjust the window layout using proportions. Is there a trick or rule of thumb I can follow when transfering an application from desktop to laptop. Thanks in advance

## How to plot a point on a globe with given longitud...

Hello! I'm working on a globe right now with worldmap, equator,0°- and 90° meridian on it. Now I want to display a point on it in the form of a circle. The point is given in longitude and latitude values, for example lon: -21.5750 and lat: -60.9340. How do I do that? If it helps, here the equation of the globe: Globe:= (lon,lat) ->(cos(lon)*cos(lat), sin(lon)*cos(lat), sin(lat)); Can someone help me please?

## Converting "Undefined" Elements of Array...

I am having difficulty with a procedure that takes an Array and returns its maximum element -- and suspect that the difficulty is due to the fact that my Array (called it A) has elements of mixed data type, i.e. some numeric and some "undefined" elements. How do I replace the undefined elements and/or get Maple to work with them?

I was thinking that I could convert them to a placeholder value of 0, since I'm maximizing?

Here's the error message, followed by a slice of my array -- you can see that there's already an undefined elements:

Error, (in maxpt) invalid input: ArrayDims expects its 1st argument, A, to be of type Array, but received [[.2500000000, .3125000000, .3620558262, .4031851184, .4375000000, .4659321892, .4891103366, .5074959503, .5214466094, undefined, .5368923611, .5381944444, .5351562500, .5277777777, .5160590278, .5000000000, .5000000000, .5000000000, .5000000000, .5000000000, .5000000000, .5000000000, .5000000000, .5000000000, .5000000000], [.2947082519, .3533020019, .3989515781, .4361746204, .4665832520, .4911091912, .5103810885, .5248604523, .5349048614, .5406428808, .5417911264, .5383316213,

## Broken MathML tag when converting from LaTeX....

Questions authored in LaTeX and converted using the facility on this site do not display properly. 'Broken MathML tag' appears where the matrix should be. The same questions converted with the old Brownstone converter are fine! Is this a problem others have had?

1/19 - 5/18

## SlideShow...

SlideShow mode in Maple 11 will not scroll down with the cursor keys or respond to page up or down. Any ideas.

## Finding the Maximizer Using Plot...

I have a function that cannot be maximized by taking the FOCs, i.e. non-convex, and I want to maximize it with respect to two variables. Say, with respect to (x,y).

I have found an example where you can extract the maximizer from plot using this approach:

> P:=plot(subs(x=0.1,subs(tau=0.3,subs(theta=1,subs(omega=0.5,payoff)))),y=0..1):
> A:=remove(has,op([1,1],P),undefined):
> MAX:=max(op(map(t->t[2],A)));
MAX := 0.330385487730942451

> points:=op([1,1],P):
> MAXPT:=select(t->t[2]=MAX,points);
MAXPT := [[0.287405284999999956, 0.330385487730942451]]

The above example is for the case where you maximize a function with respect to a single variable, y. (The value of x is fixed above; tau, theta, and omega are parameters of payoff.)

## Plotting a procedure...

I am trying to plot the following procedure in the variable s_val (with p_val and pa_val at fixed values):

> Q_opt:=proc(s_val,p_val,pa_val)
> fsolve(subs(p=p_val,subs(s=s_val,subs(pa=pa_val,FOC))),Q);
> end proc:

with no luck. I have tried the following variants of plot:

(1)

> plot(subs(p_val=0,subs(pa_val=0.6,Q_opt)),s_val=0.5..0.59,axes=BOXED);

Error, (in plot) invalid plotting of procedures, perhaps you mean plot(Q_opt, .5 .. .59, axes = BOXED)

(2)

> plot(subs(p_val=0,subs(pa_val=0.6,Q_opt)),0.5..0.59,axes=BOXED);

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

## Handling Piecewise FOCs in an Optimization Problem...

I have an optimization problem where my integration bounds depend on the maximizer and take the form max[1,Q+pa/2], where Q is the variable that I am maximizing with respect to.

For instance, my function U (utility), which I am maximizing is defined as follows:

U:=simplify(int(-(-d)^2,d=0..D_lbar)+int(-(-s/2)^2-s*(d-s/2),d=D_lbar..D_bar2(Q))
+int(-(Q-d)^2-s*Q,d=D_bar2(Q)..DD_bar2(Q)))+int(-(-pa/2)^2-s*Q-pa*(d-pa/2-Q),d=DD_bar2(Q)..1)

where

D_lbar:=s/2;
D_bar:=Q+s/2;
D_bar2:=Q->piecewise(Q+s/2>1,1,Q+s/2);
DD_bar2:=Q->piecewise(Q+pa/2>1,1,Q+s/2);

I get a piecewise FOC for U, with respect to Q, and I'm able to solve for the optimal Q, given the parameters s, p, and pa, using fsolve. For example:

## To plot a plane parrallel to a vector that goes th...

hello everyone, I'd really appreciate your help. I have to finish a maple assignment within a couple of days and i've been stuck on this question that wants me to find a plane parrallel to a vector that goes though a point. The instructor gave me the following example [code] Example 6. Find the equation of the plane perpendicular to the vector ( 5, 1, -2 ) and passing through the point ( 0, 1, -1 ). Make a plot of this plane. We use the point-normal form of the equation of a plane: dotprod([5,1,-2],[x-0,y-1,z-(-1)])=0; _ _ _ 5 x - 3 + y - 2 z = 0

## I want to define a function as the solution to the...

Hello, I am trying to do something very simple, or so I thought. From the solve help, I found this example: solve(x*t(x)+x^3-5, t); Now to my way of thinking, I have just solved an equation that gives me a function of x, namely t = t(x). But when I try to evaluate t at say, 3, I do not get the correct answer: t(3); gives the helpful response: t(3) How can I get this to work? Thank you.