WOLFRAM|DEMONSTRATIONS PROJECT

Limit Laws

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f(x)
1
x-1
x^2 -1
x^3 -1
ln(x)
ln(x^2)
(x-1)^2
sin(x-1)
sin(1/(x-1))
|sqrt(x-1)|
g(x)
1
x-1
x^2 -1
x^3 -1
ln(x)
ln(x^2)
(x-1)^2
sin(x-1)
sin(1/(x-1))
|sqrt(x-1)|
combination
sum
difference
product
quotient
k f(x)
fx
k
)\),
k constant
zoom
Pairs of functions can be combined in six standard ways. The pairs are plotted as dashed curves and their combination as a solid brown line. The limit of the combination as
x
approaches 1 is the height of the red dot.