Question

`lim_(x->0)(2x-4)/(5x)`?

Answer 1

Undefined

Explanation:

`lim_(x->0)(2x-4)/(5x)`

Divide numerator and denominator by `x`:

`(2x/x-4/x)/(5x/x)`

Cancelling:

`(2cancel(x)/cancel(x)-4/x)/(5cancel(x)/cancel(x))=(2-4/x)/5`

as: `x->0^+color(white)(888)` , `(2-4/x)/5->-oo`

as: `x->0^-color(white)(8888)` , `(2-4/x)/5->oo`

`:.`

`lim_(x->0^+)(2x-4)/(5x)!=lim_(x->0^-)(2x-4)/(5x)`

Hence:

`lim_(x->0)(2x-4)/(5x)color(white)(888)` Undefined