# Limit (G Dataflow)

Determines the left and right limits of a function at a given point.

## formula

Function to calculate. The formula can contain any number of valid variables.

Entering Valid Variables

This node accepts variables that use the following format rule: variables must start with a letter or an underscore followed by any number of alphanumeric characters or underscores.

## point

Point at which this node calculates limits.

Default: 0

## delta

Distance to the left and right neighbor of point.

delta is internally rounded to a power of 2. Take a value of delta = 1E-10 in all cases because a very small delta value can result in numerical inaccuracies.

Default: 1E-10

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## left limit

Left limit of the given function at point, which is the function value at point - delta. The accuracy is up to 8 decimal digits.

## right limit

Right limit of the given function at point, which is the function value at point + delta. The accuracy is up to 8 decimal digits.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

The function $f\left(x\right)={\left(1+\frac{1}{x}\right)}^{x}$ has the limit e (Euler) as x tends to infinity.

To find the limit of f(x) as x tends to infinity, you can instead find the limit of g(x) = f( $\frac{1}{x}$) as x tends to 0. With this in mind, you define $g\left(x\right)={\left(1+x\right)}^{\frac{1}{x}}$ and apply the Limit function to g(x) to obtain the limit value of e.

Thus, enter the following values on the panel:

formula: (1+x)^(1/x)

point: 0

The following graph shows the convergence of f(x) to e as x becomes greater.

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices