## 454 Reputation

19 years, 43 days

## Solve equation with parameters....

Maple

I just found out something which I don't understand.

Why am I getting this answer?

solve(a*x = 0, {x});
{x = 0}

When I try some similar expressions I see it behaves differently for equality and inequality.

solve(a*x <= 0, {x});...

## Plotting a filled semicircle rotated acr...

Maple

I can't solve probably very easy problem. How to plot a filled semicircle which is rotated across one axis by an angle alpha? I came to the solution which I don't consider as the best one (since e.g. it will not work for alpha=Pi/2*(odd integer)) and I believe someone of you will show me a better approach. Thank you in advance.

My solution:

`alpha := (1/6)*Pi:plot3d([x, y, y*tan(alpha)], x = -1 .. 1, y = 0 .. sqrt(1-x^2)*cos(alpha), axes = normal, labels = ["x", "y", "z"...`

Maple 16

Can somebody, please, try this command in Maple 16 (or at best Maple 16.02)?

`Student[Calculus1][FunctionChart](x*exp(1/x));`

In Maple 15 I get the graph in about 1s, however in Maple 16.02 it loads about 20s and it is even not as perfect as is in Maple 15. Furthermore, when I try to evaluate

`st:=time():Student[Calculus1][FunctionChart](x*exp(1/x));time();`

it says that it lasted only 1-2s. There is some problem...

## Simplify powers of the same base....

Maple

Is it possible to simplify for example the expression

`5^2 * 5^(1/2)`

to get

`5^(5/2)` ?

PS: I am sorry if it was asked and answered, I can't find it.

## How to plot (draw) an area efficiently?...

Maple

I would like to draw some areas between curves. I tried to use ?plots/implicitplot but I often need to use `gridrefine` option which consumes so much memory. When I want to draw e.g. the area between f and g:

`f := x-> piecewise(x < 5, 2, x-3):g := x-> piecewise(x < 4, x, 4):`

I can do:

`p:=plot({f, g}, color...`

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