## 100 Reputation

10 years, 86 days

## differentiating cosec and cot...

Maple 18

Hi Maple friends.

I am trying to differentiate these:

1. csc(x)/x

2. 3*x^2*cot(x)

From doing it by hand, I am getting:

1. -cosec(x)*(xcot(x) + 1)

2. 6x*cot(x) - 3x^2*cosec^2(x)

But Maple is giving the answer:

1. diff(csc(x)/x, x);

-csc(x)*cot(x)/x-csc(x)/x^2

2. diff(3*x^2*cot(x), x);

6*x*cot(x)+3*x^2*(-1-cot(x)^2)

My answers don't look like Maple's answers. Are they actually the same?

## get the function, from a table of values...

Maple 18

Hi Maple friends.

If I have a table of values, how can Maple provide the function?

For example:

x=10,15,20,25,30,35,40

y=2.01,4.87,6.50,9.875,14.00,18.90,24.40

How can Maple find out the y function with respect to x?

## determine intersection of two curves?...

Maple 18

Hi Maple friends.

Is there a Maple function to determine the intersection of two curves? For simple curves where the intersection is clear, I can plot them and use probeinfo to get the approximate intersection values.

But for more complex curves, where the scales are large, or the intersection point is not clear, it is difficult.

ie. intersection of y=x-3 and y=x^2-2*x-1

or intersection of y=x+1 and y=(x+1)/(x-1)

## inconsistency in expanding (a+b)^n...

Maple

Hi Maple friends.

expand( (a+b)^2 );

a^2+2*a*b+b^2

expand( (a+b)^3 );

a^3+3*a^2*b+3*a*b^2+b^3

expand( (a+4)^4 )

a^4+16*a^3+96*a^2+256*a+256 (???)

Pascal's triangle shows that 'expand( (a+4)^4 )' should have resulted in a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4

Where are the b variables in Maple's solution?