# Items tagged with calculuscalculus Tagged Items Feed

### Integrating cos(sin(theta))...

September 23 2008
0 4

I have a function when expressed in polar coordinates such that a trig function resides inside a trig function.  In calculus 101 we all learned that integrating the product or quotient of 2 or more trig functions requires integration by parts but I have never run across the case where a trig function is a function of another trig function.  Any one have any references I should consult on to learn how to handle this?

August 10 2008
0 1
```Let be q(x) some polynomial of degree = 2 in several, n variables x[i],
x to be thought as (row) vector

Can Maple provide the quadratic normalform for q (real resp. complex)?

By this it is meant that q ° f (x) equals one of

Sum( c[i]*x[i], i=1..n)
Sum( c[i]*x[i], i=1..n) + 1
Sum( c[i]*x[i], i=1..n) + x[n+1]

where c[i] in K, K = Reals or Complex (should not matter so much, except
char(K), and square roots have to exist, so Rationals(squareRoots) is fine),
and f: K^n -> K^n is affine ( = bijective and linear + shift vector)?

```

### discontinuities...

August 08 2008
0
34

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

### Function limits at domain endpoints...

August 03 2008
0
21

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

### Old Maple MWS vs. new Maple 12 results differ !...

July 17 2008
0 2
hi, i'm using an existing Maple mws that was created by some unknow version of Maple. the Maple text is show below, and the old result is the last line (0.28031703) restart; T := ->(1/8)*sqrt(x^2+225)+(1/3)*sqrt((20-x)^2+625); dT := D(T); solve(dT(x) = 0, x); evalf(%); Sols := %; Xbest := Sols[1]; solve(25/(20-x) = 15./x, x); T(%)-T(Xbest) 0.28031703 when i run in with Maple 12 Student Edition, the result I get is 11.41326364-(1/8)*sqrt(13.51659367[1]^2+225)-(1/3)*sqrt(1025-40*13.51659367[1]+13.51659367[1]^2)

### simplify(%) don't simplify...

June 11 2008
0 12

Good morning.

I've this funny problem with maple11. I get an expression as output from a calculus, and I try to simplify it with simplify(%), but simplify don't simplify and give the same expression as result.

On the other hand, If I copy the expression and paste it as argument of simplify it work fine.

Anyone know why this happens?

Thank you

S.

ps: the expression to simplify (in fact is more simple than a simplification: there are terms equals but with different sign to cancel togheter) is

### Calculus of variations, fixed endpoint problem...

May 05 2008
0 2

Any tips on how to solve fixed endpoint problems in the calculus of variations?

For instance,

Find the extremal for:

int(diff(x(t),t)^2/(t^3),t=1..2) with x(1)=2 and x(2)=17.

The correct answer is x(t) = t^4 + 1.

### Clairaut's (Young's) theorem...

April 21 2008 Maple
1
45

How can Maple arrive at the following, for an unspecified function f(x,y), without knowing sufficient conditions (eg. whether the 2nd partials are continuous)?

```> # From the ?diff help-page
> diff(f(x,y),x,y) - diff(f(x,y),y,x);
0
```

Continuity of integrands isn't generally assumed by int (there's a separate optional parameter which enables it...

### Can't get package to work...

April 05 2008
0 2

Okay, I'm just really starting to get into Maple again, but I'm having a little trouble getting a package to work.

I'm trying to take a look and review the precalculus package from the application center but it doesn't seem to work.

It's from maple 7.  The new version doesn't seem to follow through on the commands made.

### Cum laude...

March 28 2008
0
0

No, the title does not come from hornybitches.com, nor does it mean something related to sex.

### General Relativity...

March 26 2008
1
7

Special Relativity has been around for ~100 years, General Relativity for ~90 years.  I'm hoping that with the assistance of Maple and Mapleprimes I may be able to do some tensor calculus to better understand Einstein.  Perhaps the twin paradox is within my reach.  Perhaps even the orbit of Mercury.

### Do you know any antiderivative that maple can't fi...

March 02 2008
0
2

I need to find an example of a function of one variable that has an antiderivative that can be expressed very simply in terms of fuctions that a 1st-year calculus student would know, but int (command name in maple) can't find an antiderivative.

Hint: Start with the antiderivative F(x), and get f(x) by differentiating it and simplifying. You might try something involving a few square roots and logarithms or exponentials or trigonometric functions.

### Do you know any antiderivative that maple can't fi...

March 02 2008
0 6

I need to find an example of a function of one variable that has an antiderivative that can be expressed very simply in terms of fuctions that a 1st-year calculus student would know, but int (command name in maple) can't find an antiderivative.

Hint: Start with the antiderivative F(x), and get f(x) by differentiating it and simplifying. You might try something involving a few square roots and logarithms or exponentials or trigonometric functions.

### Do you know any antiderivative that maple can't fi...

March 02 2008
0 3

I need to find an example of a function of one variable that has an antiderivative that can be expressed very simply in terms of fuctions that a 1st-year calculus student would know, but int (command name in maple) can't find an antiderivative.

Hint: Start with the antiderivative F(x), and get f(x) by differentiating it and simplifying. You might try something involving a few square roots and logarithms or exponentials or trigonometric functions.

### Maplesoft Great Application Contest - Winners!...

January 23 2008
0
2

We are pleased to announce the winners of the Great Application Contest. First prize is awarded to Dr. Jason Schattman, for his entry Can a Square Roll?, an exploration of the "Renaissance Man of calculus problems", the square wheel problem. The runner-up is Prof. Mario Lemelin, for his Pré-test en Mathématique, a Maple-based questionnaire that lets beginning differential calculus students test their secondary school mathematics comprehension. These and many other Maple applications can of course be viewed on the Maple Application Center. Congratulations to both!

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