Natural logarithm ln(x) calculator finds the logarithm function result in base e which is approximately 2.718….Natural Logarithm Values Tables.

Limits are nothing but minimums and maximums in our lives. The simple idea is that we have a minimum and a maximum number of units (time, money…) we’re prepared to spend on a certain activity (work, sports, spouse…). Having limits helps us organize investments of our time, energy and other resources.

We should study limits because the deep comprehension of limits creates the necessary prerequisites for understanding other concepts in calculus.

In order for a limit to exist, the function has to approach a particular value. In the case shown above, the arrows on the function indicate that the the function becomes infinitely large. Since the function doesn’t approach a particular value, the limit does not exist.

A limit tells us the value that a function approaches as that function’s inputs get closer and closer to some number. The idea of a limit is the basis of all calculus.

If your pre-calculus teacher asks you to estimate the limit of a function analytically, you can simply set up a chart and put the number that x is approaching smack dab in the middle of it. Then, coming in from the left in the same row, systematically choose numbers that get closer to the number.

To approximate the limit of a function f(x), as x approaches a, all we have to do is take a look at the graph of f(x) where x = a, and find the approximate corresponding y-value (or function value). For instance, consider our medication example again.

Finding Limits Graphically

1. limx→c-f(x) = L to denote “the limit of f(x) as x approaches c from the left is L”
2. limx→c+f(x) = L to denote “the limit of f(x) as x approaches c from the right is L”
3. limx→cf(x) = L to denote “the limit of f(x) as x approaches c is L”

Tables of function values are great for predicting trends. All tables show limiting values.