`f(x)= |{:(cos x,,x,,1),(2sin x ,,x^(2),,2x),(tanx ,, x,,1):}|` then find the value of
`underset(xto 0)(" lim ") (f(x))/(x)`

Explanation

`f'(x)=|{:(-sin x, 1, 0),(2 sin x, x^(2), 2x),(tan x , x, 1):}|+|{:(cos, x, 1),(2 cos x, 2x, 2),(tan x, x, 1):}|`
`|{:(cosx, x, 1),(2sin x, x^(2),2x),(sec^(2)x, 1,0):}|`
`rArr" "f'(0)=|{:(0,1,0),(0,0,0),(0,0,1):}|+|{:(1,0,1),(2,0,2),(0,0,1):}|+|{:(1,0,1),(0,0,0),(1,1,0):}|=0`
`"Now ,"underset(xrarr0)lim(f(x))/(x)=underset(xrarr0)limf'(x)(as f(0)=0)`
`f'(0)=0`