Limit Laws

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.