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Limit

Limit (WMA link)

Limit[expr, x->$x_0$]

gives the limit of expr as x approaches $x_0$.

Limit[expr, x->$x_0$, Direction->1]

approaches $x_0$ from smaller values.

Limit[expr, x->$x_0$, Direction->-1]

approaches $x_0$ from larger values.

• • Limit[x, x->2]

• • Limit[Sin[x] / x, x->0]

The limit value can change depending on which direction the limit is approached from.

Consider this inverse x function:

• • Plot[1/x, {x, -10, +10}]

When coming to zero from positive values:

• • Limit[1/x, x->0, Direction->-1]

But when coming to zero from negative values:

• • Limit[1/x, x->0, Direction->1]

A limit can be Indeterminate:

• • Limit[Tan[x], x->Infinity]