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"Let "g(x)=|{:(f(x+c),f(x+2c),f(x+3c)),(...

`"Let "g(x)=|{:(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c)):}|,`
where c is constant, then find `lim_(xrarr0) (g(x))/(x).`

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The correct Answer is:
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`g(x)=|{:(f(x+c),f(x+2c),f(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c)):}|`
`therefore" "g(0)=0`
`therefore" "underset(xrarr0)lim(g(x))/(x)" "((0)/(0)from)`
`=underset(xrarr0)lim(g'(x))/(1)" (using L' Hopital rule)"`
`g'(0)`
`"Now, "g'(x)|{:(f'(x+c),f'(x+2c),f'(x+3c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c)):}|`
`therefore" "g'(0)=|{:(f'(c),f'(2c),f'(2c)),(f(c),f(2c),f(3c)),(f'(c),f'(2c),f'(3c)):}|=0`
`therefore" "underset(xrarr0)lim(g(x))/(x)=0`
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