Question

Question #1ec73

Answer 1

`lim_(x to oo) (x^2/2-x)(0^2/2-0) = 0`

Explanation:

We want to find:

`lim_(x to oo) (x^2/2-x)(0^2/2-0)`

If we examine the limit function, we have;

`(x^2/2-x)(0^2/2-0) = (x^2/2-x)(0) = 0`

Hence,

`lim_(x to oo) (x^2/2-x)(0^2/2-0) = 0`

Answer 2

`lim_(xrarroo) ((x^2)/2-x)((0^2)/2-0)=color(green)(0)`

Explanation:

`((0^2)/2-0)=0`

Any defined value multiplied by `0` equals `0`.

The possible conceptual problem here is in trying to take the given expression as:
`color(white)("XXX")oo xx 0 = ???` (undefined)
but
`color(white)("XXX")lim_(xrarr0)` does not mean that `x` is ever actually `=0`
and for any value `barx!=0`
`color(white)("XXX")((barx^2)/2-barx)` is defined, say as some (defined) value `v`
`color(white)("XXX")`and
`color(white)("XXX")v xx 0 = 0`