Version:

Last Modified: March 15, 2017

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

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 at which this node calculates limits.

**Default: **0

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 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.

**Default: **No error

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

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

The function
$f\left(x\right)={(1+\frac{1}{x})}^{x}$ 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
$g\left(x\right)={(1+x)}^{\frac{1}{x}}$ 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