Question

Find the limit lim as x approaches 0 from the left (1/x -1/|x|)

Answer 1

If
`x\to0^-`, then we're considering values of
`x` where
`x<0`. When
`x` is negative, we have
`|x|=-x`. So,

`\displaystyle\lim_(x\to0^-)\frac1x-\frac1x=\lim_(x\to0^-)\frac1x-\frac1x=\lim_(x\to0^-)0=0`