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Show that f(x)={(sin3x)/(tan2x3/2,ifx=0...

Show that `f(x)={(sin3x)/(tan2x3/2,ifx=0),ifx<0(log(1+3x))/(e^(2x)-1),ifx >0i scon t inuou sa tx=0`

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`f(0^+)= f(0^-) = f(0) = 3/2`
`f(0^+) = lim_(x->0) (log(1+3x))/(e^(2x) - 1)= 0/0`
`= lim_(x->0) ((1/(1+3x)xx 3)/(0^(2x) xx2))`
`= 3/2 `
`f(0^-) = lim_(x->0) (sin 3x)/(tan2x) = 0/0`
`= lim_(x->0) (3cos 3x)/(2sec^2 2x)= (3 xx cos 0)/(2 xx sec^2 0) = 3/2`
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