Question

Question #4e891

Answer 1

1

Explanation:

`lim (x^2-7x+10)/|x^2-4|`
`x->oo`

As `x` tends to `oo` , therefore `|x^2-4|` can be replaced by `x^2-4`

`lim (x^2-7x+10)/(x^2-4)`
`x->oo`

This is `oo/oo` indeterminate form,
This can be easily solved by dividing the numerator and denominator by highest power of `x` in the expression (Here, `x^2`)

`lim ((x^2)/x^2-(7x)/x^2+(10)/x^2)/((x^2)/x^2-4/x^2)`
`x->oo`

`lim (1-(7)/x+(10)/x^2)/(1-4/x^2)`
`x->oo`

As `x` tends towards `oo` , `1/x` as well as `1/x^2` tends towards `0`.

`lim (1)/(1)`
`x->oo`

Answer:`1`