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Evaluate the following limit: lim(x->0)(...

Evaluate the following limit: `lim_(x->0)(log(3+x)-"log"(3-x))/x`

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`lim_(x->0)(log(3+x)-log(3-x))/x`
`=lim_(x->0)log((3+x)/(3-x))/x`
`=lim_(x->0)log(1+(3+x)/(3-x)-1)/x`
`=lim_(x->0)log(1+(3+x-3+x)/(3-x))/x`
`=lim_(x->0)log(1+(2x)/(3-x))/x`
`=lim_(x->0)log(1+(2x)/(3-x))/((2x)/(3-x)xx(3-x)/2)`
`=(1 xx 2)/(3-0)`
`=2/3`
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