Evaluate `lim_(x-> 0) (tan3x-2x)/(3x- sin^2 x)`

1.	Evaluate `lim_(x-> 0) (tan3x-2x)/(3x- sin^2 x)`
Answer» `lim_(xto0)((tan3x-2x)/(3xsin^(2)x))` `=lim_(xto0)(((tan3x)/(3x)-2/3))/((1-(1)/(3).(sinx)/(x).sinx))" "["dividing num. and denom. by 3x"]` `=((lim_(xto0)(tan3x)/(3x)-2/3))/({1-1/3lim_(xto0)(sinx)/(x).lim_(xto0)sinx})=((1-(2)/(3)))/(1-((1)/(3)xx1xx0))=(((1)/(3)))/(1)=1/3.`

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