# Mathematical Analysis

# The functions for the online resolution of analysis exercises are divided into three sections:

### Limits

The required limit is calculated by providing not only the result but also the graphical representation. If you are asked to tend the X towards a value that is not an accumulation point of the domain or you cannot tend it to the required direction, the system notices the error and does not calculate the limit.

### Derivative

The derivative of the given function and of the chosen order is calculated (up to the 20th order) by giving back the derivatives of all orders until the one requested. The software also gives back the graph of the given function together with that of the derivative. You can also ask to calculate the derivative at a specific point. The software calculates the domain of both the function and of all the calculated derivatives

## Complete studies

### Complete study of a function

The complete study of the given function is performed

### Study of the domain of a function

The study of the domain of a function is performed by showing the details of the calculations deriving from the imposed conditions. The details of the calculations are not shown in the complete study of the function to not to make the document too long, thus if you also want those you must refer to this function

### Study of the points of discontinuity of a function

The points of discontinuity of the given function are studied showing more details of those shown by carrying out a complete study. In particular, all the points that could be points of discontinuity are considered and therefore they are verified one by one if they are or not points of discontinuity and in case showing the species and explaining the reasons for this choice.

### Study of the sign of the first derivative

The study of the sign of the first derivative is performed and therefore the increasing and decreasing of the function. Finally, the points of relative maximum and relative minimum (stationary or not) and the points of inflection with horizontal tangent are studied.