Limit (Not in Base Package)

Determines the left and right limits of a 1D function at a given point. Details

point is the point at which the limits have to be calculated. The default is 0.0.
delta is the distance to the left and right neighbor of point. The default is 1E - 10.
formula is a string describing the function under investigation. You can use any valid symbol as the variable name. Refer to Formula VI Variables for valid symbols.
left limit is the left limit of the given function at point. The accuracy is up to 8 decimal digits.
right limit is the right limit of the given function at point. The accuracy is up to 8 decimal digits.
ticks is the time in milliseconds to analyze the formula and to produce limits. Usually, the time is negligible for the limit operations.
error indicates the accuracy of formula, which is verified by the Function VIs.

Limit Details

The algorithm calculates only the two values f(pointdelta) and f(point + delta). Furthermore, delta is internally rounded to a power of 2.

Note  A very small delta value can result in numerical inaccuracies. You should take a value of delta=1E–10 in all cases.

The function

f(x) = (1 + 1/x)^x

has the famous limit e (Euler) if x tends to infinity. You can use the Limit VI to determine the Euler number if you define

g(x) = (1 + x)^(1/x)

for small positive x. By entering

(1+x)^(1/x)

in the formula control on the front panel, you can find the limit. The following diagram shows the convergence of f(x) to e.