1.

Find the value of `1//x`for the given values of `xdot``x >3`(ii) `x

Answer» (i) We have `3 lt x lt oo`
`implies (1)/(3) gt (1)/(x) gt (1) /(to oo)`
`implies 0 lt (1)/(x) lt (1)/(3)`
(ii) We have ` -oo lt x lt -2 `
`implies (1)/(to -oo)gt (1)/(x) gt (1)/(-2)`
`implies 0 gt (1)/(x) gt -(1)/(2)`
`implies -(1)/(2) lt (1)/(x) lt 0`
(iii) `x in (-1,3) -{0}`
`implies x in (-1,0) cup (0,3)`
For `x in (-1,0), ` we have
`(1)/(-1) gt (1)/(x) gt (1)/(to 0^(-))`
`implies -1 gt (1)/(x) gt -oo`
`implies -oo lt (1)/(x) lt -1 " " `(1)
For `x in (0,3), ` we have
`(1)/(to 0^(+)) gt (1)/(x) gt (1)/(3)`
`implies oo gt (1)/(x) gt (1)/(3)`
`implies (1)/(3) lt (1)/(x) lt oo " " ` (2)
From (1) and (2) , `(1)/(x) in (-oo, -1) cup ((1)/(3), oo)`


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