Continuity

Explores continuity of a function f (x) by comparing the value of the function at x=c to values of the function for x approaching c.
How to use   ||   Examples   ||   Other Notes


How to use The text input field for f (x) can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates. The text input fields for c and x can accept real numbers in decimal notation.
Examples
Polynomial
f (x)=x2
c=1, x=2
Exponential
f (x)=ex
c=0, x=1
Trigonometric
f (x)=sin(x)
c=0, x=1

Other Notes
The values of c and f (c) are indicated in the graph by orange lines, with the red point in the graph shown at the point (c,f (c)). The values of x and f (x) are indicated in the graph by blue lines. The table shows values of f (x) for x starting at the given value and approaching c -- in particular, the values x, c+(x-c)/2, c+(x-c)/4, etc. These values are indicated in the graph by green lines.