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If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2)...

If `f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}|`, then `lim_(xto0)(f(x))/(x^(2))=`

A

(a) `0`

B

(b) `3`

C

(c) `2`

D

(d) `1`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}|`
`:.(f(x))/(x^(2))=|{:((sinx)/(x),cosx,(tanx)/(x)),(x^(2),x^(2),x),(2,1,1):}|`
`:.lim_(xto0)(f(x))/(x^(2))=|{:(1,1,1),(0,0,1),(2,1,1):}|=1`
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