# A limit problem. (Is something wrong with matlab?)

1. Oct 13, 2007

### oahsen

With the following code segment ;
limit((sin(z+h)-sin(z))/h,h,0)
matlab gives the result cos(z). (which is the differential of the sin(z)).
However, with the code ;
limit((sinh(z+h)-sinh(z))/h,h,0)
matlab gives an absurd result;
limit((sinh(z+h)-sinh(z))/h,h = 0)
newertheless, the result should be cosh(z). Why does matlab makes such a wrong calculation also what is the meaning of this result? Does anybody have an idea about that?

2. Oct 13, 2007

### atqamar

I tried the same code, and i got:

ans=
NaN

I don't know why this answer is given. However, if you are looking for the derivitive of a function, try this line:

> syms x; diff(sinh(x))
ans =
cosh(x)

3. Oct 14, 2007

### Dick

Just for the record, Maxima does it right.

(%i1) limit((sinh(x+h)-sinh(x))/h,h,0);

gives exp(-x)*(exp(2x)+1)/2;

4. Oct 14, 2007

### oahsen

actually this is the problem. The teacher asks us to find the derivative with;
syms x; diff(sinh(x)) and after that finding it with;
syms z h; limit((sinh(z+h)-sinh(z))/h,h,0)

and he wants us to comment on the difference.

With my matlab(R2007a) I find the first result as cosh(z) as expected however with the second code it gives me ;
limit((sinh(z+h)-sinh(z))/h,h = 0).

Some of my friend said that Maxima finds the correct result. I wonder if it is something about the limit algorithm of Matlab or I do not know? What kind of comment can I write for the difference?

5. Oct 14, 2007

### HallsofIvy

Staff Emeritus
I'm wondering if you didn't accidently enter a "=" instead of "," and MatLab just echoed it back to you.

6. Oct 14, 2007

### oahsen

I checked it 1000 times. This is the copy of the command window;

>> syms z h;
>> limit((sinh(z+h)-sinh(z))/h,h,0)

ans =

limit((sinh(z+h)-sinh(z))/h,h = 0)

7. Oct 14, 2007

### atqamar

If limits have to be used to find the derivitive, use the exponents definition of sinh(x) and find the limit:

>> syms z h; limit((((exp(z+h)-exp(-z-h))/2)-((exp(z)-exp(-z))/2))/h,h,0)
ans =
(1/2*exp(2*z)+1/2)*exp(-z)

The answer, when simplified, is cosh(x).